Talk:Cosmic inflation

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Has anyone come across a resolution concerning temporal consequences of cosmic inflation making the universe expand faster than the speed of light? i.e., if the universe's outer boundary is moving that fast, then it can travel backward in time, causing an implosion, a duplication of all matter, and massive temperature/density increase until the inflationary period ended.

Which might not be a bad thing, as it would increase information transfer between the universe's parts, but has this been addressed at all?

Apparently there is no temporal consequence from SR, since relativistic time reversal only applies to things moving through space but not the expansion of space itself.

The speed of light can be defined only in terms of the metric tensor; inflation theory uses a metric with nonzero curvature; making that argument invalid.

63.205.40.227 02:05, 4 Feb 2004 (UTC)

The metric tensor is well defined in inflation, and nothing can move through space faster than the speed of light. But here space itself os the thing that moves, causing the distance which seperates two stationary points to grow bigger and bigger, so that one point would be seen from the other point as if it moves faster than the speed of light. Shokopuma 19:54, 26 April 2006 (UTC)Reply

---

I think this overstates the case. WMAP supports cosmic inflation but it is one of several supporting bits of evidence.

This theory was revealed to be correct with NASA's historic February 11, 2003 release of data collected from the Wilkinson Microwave Anisotropy Probe (WMAP).

---

I have a question. If it's true that the Universe is expanding in a accelerated rate, then would cosmic inflation explain universe's current accelerated expansion rate?

No. Inflation refers to a very brief period in the early universe when the rate of expansion of the universe increased dramatically. As soon as inflation ended, the universe continued expanding at a more conservative rate. However, if everything in the universe attracts everything else gravitationally then we would expect the expansion to slow down over time through this mutual attraction between all objects. The 'fact' (still some controversy over this) that the expansion is not slowing down but rather accelerating means that despite gravity trying to hold everything together, there is another force at work driving this 'anti-gravity' effect and increasing the expansion rate. This new force is generally referred to as dark energy (not to be confused with dark matter) and is thought to make up about 70% of the critical density required to close the universe.

However, some people think that dark energy doesn't exist at all, and that the solution is to modify general relativity to modify the action of gravity over cosmological distance scales. DH79 11:53, 14 October 2006 (UTC)Reply

Actually that's not quite the complete picture -- the current "accelerating" expansion of the universe is a lot like inflation in that both may be modelled by a constant Hubble factor. In the modern picture the universe expanded very rapidly with a constant Hubble factor during the inflationary phase: then the expansion slowed with the decrease of the Hubble factor: now the decline in the Hubble factor is/has tailed off and the expansion has stablised again -- albeit at a much lower level than previously. --Michael C. Price ^talk 21:51, 14 October 2006 (UTC)Reply

Thanks for that extra info Michael. Just one further point - am I right in thinking that the mechanism that drove inflation (scalar field in a potential well) is not thought to be the same reason that we now have an acceleration of the expansion rate (energy density of the vacuum due to Planck scale quantum fluctuations)? These may be two ways of expressing the same physics, but if so I'm unaware of it. DH79 17:02, 15 October 2006 (UTC)Reply

Yes, the mechanisms are different, but that's probably all we can say with certainty. The current accelerated expansion may be due to a cosmological constant (a constant term in the Einstein field equations) and early universe inflation may be due a scalar field (the Higgs?), but no one knows for sure about either -- yet. --Michael C. Price ^talk 17:51, 15 October 2006 (UTC)Reply

negative pressure vacuum energy density

What is vacuum energy density? Do you mean false vacuum? How could vacuum itself (with no mass-energy) contain pressure? Do you mean that spacetime has an energy which is always positive (or non-zero)? Is it because according to Einstein's theory of general relativity, bodies create the space around them? -- Orionix 22:30, 9 Mar 2005 (UTC)

Vacuum energy is not really related to the false vacuum -- a true vacuum can have an energy density as well. One thing that quantum field theory has taught us is that there is energy in a vacuum -- see Casimir effect. With energy comes pressure, since pressure is just the work done to change the volume of a box. In the case of vacuum energy, the pressure is negative since increasing the volume of the box increases the energy, and so you must do work on the box (with an ordinary gas of particles, it is the opposite). Gravity, however, is strange, and making spacetime have positive energy actually makes the expansion accelerate. See the explanation under cosmological constant in dark energy. --Joke137 17:02, 10 Mar 2005 (UTC)

Hi, thanks for the explanation.

I'm really not an expert in the mathematics of QFT but i know the basic idea which is that at high energies matter is better described by fields rather than by classical means.

This great work may also teach us one day that discrete particles do not exist and that all matter is a wave structure, continuous in the space it occupies (or is part of).

I was wondering whether cosmic inflation could explain how the universe came into being and also why it's accelerating. According to what i understood, cosmic inflation occurred during the time of superunification (Planck era, ${\displaystyle 10^{43}}$  second) or grand unification (GUT era, ${\displaystyle 10^{35}}$  second) while the universe existed in a state of nonzero energy density (also called false vacuum). A false vacuum is a combination of mass density and negative pressure that results gravitationally in a large repulsive force (antigravity).

A problem with this theory is the "graceful exit" (the fine-tuning). As of 2005, do you have any idea of how this problem could be solved in inflation? -- Orionix 18:30, 14 Mar 2005 (UTC)

In answer to some of your questions... Inflation does not provide any explanation of what happened before inflation. In fact, some theorists think that generating the necessary initial conditions for inflation to start is a major problem for inflation. There was indeed a much larger energy density during the early universe inflation than the energy density which we observe in the universe today, but this is not necessarily a false vacuum. The original idea by Guth did use a false vacuum and this lead to the so called graceful exit problem. However, that was abandoned in favor of other models which do not suffer from this problem. There is still a fine tuning problem with any known inflation models, where fine tuning has a technical meaning, but this is not the graceful exit problem of the old inflation based on a false vacuum. -- matt 19 Mar 2005

Removing link

Removing link 13 things do... The Link dose not link to anything related to the article. Johan Bressendorff

Gravitational energy density

Latest comment: 19 years ago14 comments3 people in discussion

A problematic quote has been inserted a couple of times:

A generic property of inflation is the balancing of the negative energy of the gravitational field, within the inflating region, with the positive energy of the inflaton field to yield a post-inflationary universe with negligible or zero energy density. Alan Guth says "Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully. In this appendix I will explain how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative." (See Guth's "The Inflationary Universe" (ISBN 0224044486) Appendix A) It is this balancing of the total universal energy budget that enables the open-ended growth possible with cosmic inflation; during inflation energy flows from the gravitational field (or geometry) to the inflaton field -- the total gravitational energy decreases (becomes more negative) and the total inflaton energy increases (becomes more positive). But the respective energy densities remain constant and opposite since the region is inflating. Consequently inflation explains the otherwise curious cancellation of matter and gravitational energy on cosmic scales which is a feature of a zero-energy universe, which is consistent with astronomical observations.

There is no such thing as the energy of the gravitational field in general relativity. This is a big problem, and people have come up with various constructions that allow energy to be measured in some circumstances, like the ADM energy. But in general it is problematic, and while I don't know the context of the quote, I think Guth is here giving a hand-waving description of how inflation functions. But I really don't know if the quote is appropriate, so I reverted the edits. At the very least, more context is needed. –Joke 15:23, 14 February 2006 (UTC)Reply

It is not true that there is no such thing as the energy of the gravitational field in GR. To maintain conservation of energy the gravitational field must be assigned an non-tensoorial energy (generally negative) although such an energy density is not tensorial neither is it absent. Such dismissal is simplistic. The context of the quote by Alan Guth is clear from the content of the quote and title of the book, namely free-lunch aspect of inflation, a central concept and one which Guth (and others) frequently mention in both technical and popular expositions of inflation. The removal of the text is therefore unjustified on the stated grouds. However, providing more context is never a bad idea. -- MCP—The preceding unsigned comment was added by 82.2.22.65 (talk • contribs) .

I disagree. Conservation of energy is simply the statement that the stress-energy tensor is covariantly conserved, which has nothing to do with general relativity or the Einstein field equations. And I've not sure what you mean by "non-tensorial energy". Perhaps you mean that in an asymptotically flat spacetime it is possible to write the Einstein equations in such a way that they look like a wave equation plus a contribution from a Lorentz invariant, non-tensorial quantity that looks an awful lot like the stress-energy tensor of the gravitational field. This gives you the ADM energy I alluded to above. I'm not sure if it is possible to do the same in a FRW spacetime or an asymptotically de Sitter spacetime, but it is certainly not possible to do it in general, since there is no general notion of energy in general relativity. –Joke 19:22, 14 February 2006 (UTC)Reply

Guth evidently disagrees. His quote continues: "......the energy of a gravitational field is unambiguously negative. The argument will be described [in the appendix] in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity." Nor is the sci.physics FAQ as certain that energy conservation is meaningless in GR, rather it says (and I paraphrase) that it depends on what you mean by energy and how you define it. By non-tensorial I mean that any resultant energy density and time-conserved integral is frame dependent, although the integral is conserved with time in a particular frame; however this should not disturb us (although it evidently does disturb a lot of people) since many useful quantities in physics are frame-dependent. All that is needed in the inflation article is a rider to the effect that energy conservation in GR is controversial, but that if we accept it then gravitational energy is "unambiguously negative" etc etc. -- MCP—The preceding unsigned comment was added by 82.2.29.195 (talk • contribs) .

The sci.physics FAQ says, regarding gravitational energy, "for these reasons, most physicists who work in general relativity do not believe the pseudo-tensors give a good local definition of energy density, although their integrals are sometimes useful as a measure of total energy." The pseudo-tensor, by the way, is one defined by Landau and Lifshitz in 1947. The fact is that there is no generally covariant definition of energy in general relativity. Not having general covariance is much worse than frame dependence: it doesn't merely depend on what foliation of spacelike hypersurfaces you're using to measure energy, it depends on the coordinates you're using, too! In limited situations, such as asymptotically flat spacetimes, it is possible to evade these restrictions, but in general it is not.

No, the ordinary divergence of the Landau-Lifshitz gravitational + matter pseudotensor vanishes in all frames; the divergence of the pseudo-tensor is itself a tensor. Therefore the gravitational energy/momenta are defined in all frames; its 4-flow across any closed hypersurface is identically zero.--Michael C Price 15:14, 6 May 2006 (UTC)Reply

Therefore, it is dishonest to talk about gravitational energy.

No, see above point.--Michael C Price 15:14, 6 May 2006 (UTC)Reply

In the context of inflation, it could be true (I don't know) that one can define energy in asymptotically FRW or de Sitter spacetimes. I wish I knew what Guth meant by "unambigiously negative" – perhaps the pseudo-tensor obeys some energy condition.

Yes, the condition obeyed is, I'm sure familar to you:

${\displaystyle 8\pi G\rho +\gamma +-3H^{2}=0}$ 

where rho is the inflaton energy density and other terms are defined below. For simplicity flatness assumed; extra term otherwise. The gravitational energy density is in the Hubble term: ${\displaystyle -3H^{2}}$  — -- MCP

The preceding unsigned comment was added by 82.14.0.213 (talk • contribs) .

Appendix A of his book only talks about Newtonian gravity, where it is easy enough to define energy. It seems that in his writings he refers to a 1932 paper of Tolman [1] but not to any of the various attempts to define energy in general relativity. Because of the problematic nature of these efforts, I think they are best left out of the article. –Joke 21:59, 14 February 2006 (UTC)Reply

Guth is referring to the fact that a physical gravitating source (that is something with a non-zero stress tensor) will positively curve space (which is another way of saying that the gravitational energy in unambiguously negative if the far-field limit is defined as a background zeroed in the normal way). --ScienceApologist 23:18, 14 February 2006 (UTC)Reply

That's true, but it's hard for me to see what it has to do with inflation. What is the gravitational energy density of the de Sitter universe? –Joke 23:24, 14 February 2006 (UTC)Reply

Any gravitational part of the inflaton field (apart from that which can be shoved into a scalar field) will have a negative gravitational energy density. --ScienceApologist 23:32, 14 February 2006 (UTC)Reply

What do you mean by gravitational part of the inflaton field? In most of the models I've seen, the whole thing is a scalar field. Even in the curvaton model, it's just a scalar field coupling to the Einstein-Hilbert term. –Joke 17:27, 15 February 2006 (UTC)Reply

Inflation has an entire set of models that can be applied with as many moments of the field you want including linear, quadratic, etc. Any "generic" inflation model includes contributions that both gravitate and contributions that inflate. If you consider the inflaton field to be simply the scalar part then that's that, but if you are interested in characterizing the actually dynamics of inflation then the "inflaton field" is everything in the universe including potentially pesky stuff that isn't a part of the scalar field. That's how I remember modeling inflationary scenarios, anyway. --ScienceApologist 19:46, 15 February 2006 (UTC)Reply

I must say, I don't really understand what you are referring to here. The inflaton is just a scalar field in the vast majority of models. The potential energy of that scalar field causes the universe to expand exponentially. The flatness of the potential energy, as a function of the field, causes it to continue to do so for an extended period. The contributions that "gravitate" you are referring to are perhaps the perturbations of the homogeneous scalar field? (Actually, because of gauge invariance, there is a degeneracy between fluctuations of the Newtonian potential and fluctuations of the scalar field, and one is usually eliminated, often the scalar field – is this what you're talking about?) –Joke 23:25, 15 February 2006 (UTC)Reply

Yes, I agree. It is not dishonest to talk about gravitational energy. In a de Sitter universe (which is all we are concerned about here) the gravitational energy density is:

${\displaystyle -3H^{2}/8\pi G}$ 

${\displaystyle G}$  = Newton's constant

${\displaystyle H}$  = Hubble's expansion factor

Note the negative sign! —The preceding unsigned comment was added by 82.14.0.213 (talk • contribs) .

You could apply the same reasoning to any FRW universe to get the energy density.

Which is no doubt how Landau and Lifshitz were able to show that in any closed universe the gravitational and matter energies cancelled exactly (Guth, ibid p273). Previously this had just been seen as a curious mathematical result; in the aftermath of inflation it takes on physical signficance in a "free-lunch" universe. -- MCP

That doesn't make it sensible! While this definition works in any FRW spacetime without spatial curvature because there is a preferred foliation in terms of flat, spacelike hypersurfaces. In that case, in appropriate coordinates, this is the Hamiltonian constraint in canonical gravity. This only works because there are preferred coordinates in FRW universes. In a more general situation, it depends on your coordinate system (i.e. it is not gauge invariant). Maybe the Laundau-Lifshitz pseudotensor obeys some general energy conditions, but the Friedman equation is not enough for the general case. Even in the de Sitter case, how would you define it if you were handed the space in the closed or static slicing? –Joke 17:27, 15 February 2006 (UTC)Reply

We are not concerned with the more general cases; inflating universes are very symmetric, with a natural choice of preferred comoving frames. In them, as in Newtonian gravity, the gravitational field can be assigned an energy density. Moving from flat to closed (or hyperbolic) we have to add a curvature term to get the gravitational energy density (a side issue, though, since spatial curvature will rapidly vanish under inflation as spatial flatness is achieved). -- MCP

On this issue, see also the comments by User:Hillman at Talk:Cooperstock's Energy Localization Hypothesis. –Joke 23:03, 25 August 2006 (UTC)Reply

Note Hillman's comment:

There is no doubt that in the end, general relativity does respect conservation of energy.

See also Stress-energy-momentum pseudotensor and note that conservation of energy-momentum holds quite generally:

the total energy-momentum crossing the hypersurface of any closed space-time hypervolume vanishes.

The objection to the use of pseudotensors is quite mistaken since it is the derivative of the Landau-Lifshitz pseudotensor which is used and this entity is a tensor (which vanishes everywhere even in an arbitary geometry). --Michael C. Price ^talk 05:02, 26 August 2006 (UTC)Reply

Arrow of time, second law of thermodynamics

Latest comment: 19 years ago3 comments2 people in discussion

This is a complex debate, but two things seem clear

• While gravity may not strictly break the second law of thermodynamics, it can certainly circumvent it through mechanisms like cosmic inflation which dilute entropy, sending the entropy density to (near) zero.

I agree --Michael C Price 19:09, 2 May 2006 (UTC)Reply

• Talking about whether gravity conserves energy or not is meaningless (see above). The fact is, that the stress-energy tensor is covariantly conserved in GR, which is the analogue of classical energy conservation. You can, in some situations, define a total energy that is conserved, but this concept is clearly not meaningful in all situations, and there is no such thing as the local gravitational energy density. See the extensive discussion above.

–Joke 19:04, 28 March 2006 (UTC)Reply

My unanswered points (yes, see previous discussion!) testify that the issue of gravitational energy conservation is not as meaningless or as simplistic as you've presented here. --Michael C Price 19:09, 2 May 2006 (UTC)Reply

Graceful Exit Problem

Latest comment: 19 years ago2 comments2 people in discussion

I'd like a little clarification on the graceful exit problem, if anyone can provide it. Two statements of the problem: "As noted by Guth himself [53], however, collisions of the walls of very large bubbles should lead to an unacceptable destruction of homogeneity and isotropy in the universe after inflation."[2] The article he cites is [3], and says that reheating requires bubble collisions that won't occur because the bubbles of the same size get pushed apart. However, he mentions percolation as a possibility (which would involve all the bubbles clustering together and creating an infinite region of true vacuum), and I wonder if that would create unaccaptable CMB fluctuations?

So, the question... can the graceful exit problem be restated as "Bubbles of true vacuum are created in the false vacuum but remain cold because inflation pushes these regions away from each other much faster than they grow." ? Also, is bubble collision ruled out as a reheating mechanism in other models (e.g. because of the ___domain wall problem)? --Keflavich 20:05, 4 May 2006 (UTC)Reply

Yes. I have tried to clarify this. There is something called new old inflation which is supposed to alleviate this problem, but it is probably not yet significant enough for inclusion in the article. –Joke 17:41, 18 May 2006 (UTC)Reply

Expert wanted?

Latest comment: 19 years ago1 comment1 person in discussion

User 86.141.57.167 (talk · contribs) added an "expert wanted" template on the article page. I do not find any confirmation this is the case. There are two points discussed here in May but neither in recent few days. Therefore I'll revert his edit for now, at least until 86.141.57.167 explains his/her edit. If any other user feels the template should be there, please fell free to put it back. Friendly Neighbour 10:24, 17 May 2006 (UTC)Reply

Some comments

Latest comment: 19 years ago4 comments3 people in discussion

• Someone added the assertion that Andrei Linde believes inflation can be past eternal. I do not dispute this, but is there a source?

Since it just needs a source why not leave it in and add a citation needed tag? -- that way someone is more likely to supply it. And yes, I read about Linde's views but don't have the cite immediately to hand.--Michael C Price 21:56, 15 June 2006 (UTC)Reply

• • Here is a source: Andrei Linde, "Inflation and String Cosmology," eConf C040802 (2004) L024; J.Phys.Conf.Ser. 24 (2005) 151-160 (available from arXiv:hep-th/0503195 v1 24 Mar 2005). Not sure if it has actually been peer reviewed, but it was presented at different technical symposia, and Dr. Linde does discuss in this paper his opinion that even though any particular past-directed geodesic must have finite length, there is no reason to conclude that there must be an upper limit on that length, so inflation can be eternal in the past. 138.162.5.12 17:33, 25 July 2006 (UTC)Robert PreisserReply
    • Thanks. Have added it to article. --Michael C. Price ^talk 01:11, 7 August 2006 (UTC)Reply

• The description of hybrid inflation was incorrect. It is eternal, just like new inflation. In fact, it is not clear that it is possible to construct a model of inflation that is not eternal.
• Inflation should not be thought of as a rapid cooling. It has a de Sitter temperature on the order of 10¹⁶ GeV.

–Joke 21:45, 15 June 2006 (UTC)Reply

Not necessarily. Read page 13 of this: http://arxiv.org/PS_cache/hep-th/pdf/0402/0402051.pdf . It says that most models of hybrid inflation are not eternal.

FYI: Someone signing as ScienceApologist can not be located by user talk and has sent me a message. User:Malangthon

Merge

Latest comment: 19 years ago2 comments2 people in discussion

I have suggested that inflationary cosmology be merged into this article, since they seem to be essentially the same thing. Salmar 02:25, 7 August 2006 (UTC)Reply

Yes, that is a no brainer. I was bold and did it. –Joke 16:00, 9 August 2006 (UTC)Reply

Kinematic inflation

Latest comment: 19 years ago3 comments1 person in discussion

New section by an obssesive "Milne Cosmology" pusher , as far as I can see. Nothing to do with inflation. --Michael C. Price ^talk 17:44, 9 August 2006 (UTC)Reply

Milne Cosmology pusher? Do you know, until a month ago, I had been arguing this cosmology for five years and nobody ever identified me as a Milne Cosmology pusher. Well, since nobody else seems to be pushing it, and to my knowledge, nobody has ever given reason to discount Milne's Cosmology, I have to do it myself. What exactly is it that you wish inflation to do if not to move the boundaries of the universe to a position further than would be allowable by the speed of light? This has everything to do with inflation. --Jonathan Doolin

Your insert contained factual errors and irrelevancies. For instance you state (without sources):

Part of the difficulty of describing inflation in the Standard cosmological model is that the standard model aspires to describe the shape of the universe from ALL reference frames at the same time.

This is just plain incorrect. Ever heard of the co-moving frame of reference?

Consider the balloon model that Eddington originally made popular. In this, he represents all particles of the universe "in" the surface of a balloon, thus obtaining a homogeneous distribution of matter with no center. By doing so, he is attempting to treat all of the particles of the universe from the viewpoint of an omniscient observer who sees all of the particles at once at some meta-instant of time. This, I would call aspiring to describe the shape of the universe from all references frames at the same time.

Also, Milne describes how homogeneity can be achieved by taking each observer associated with a particular event where the observer is at a specified density. By defining a coordinate system based on these events, you have constructed a geometry where the universe is homogeneous. However, this also describes the universe from all reference frames at the same time (unless some reference frames are not occupied by any observers.)

Unfortunately, you'll probably not find a book based on the standard model which is quite so clear on what the standard cosmological model is aspiring to do. These models generally begin by assuming universal homogeneity, and they must either mean homogeneity in terms of a single Euclidian space, or homogeneity in some Riemannian geometry.

If the model assumes homogeneity in Euclidian space, then universal homogeneity can only be accomplished in a static universe, thus all observers are comoving, and Hubble's Law does not apply, (redshifts would have to be caused by some other effect besides recession velocity.) I would regard this as highly unlikely.

If the model assumes homogeneity in any other Riemannian geometry, it is an attempt to treat all reference frames at the same time. Milne calls this a "mixed" coordinate system, where coordinates are established by observers who are at different locations and traveling at different speeds.

Your efforts would be better rewarded if you created a Milne Model article and explained there why it is so wonderful (as indeed it may be). --Michael C. Price ^talk 20:55, 9 August 2006 (UTC)Reply

As time permits, I will. Thank you. If you know any other obsessive Milne Pushers, please let me know. I am not in the loop and would very much like to be.

Your explanation seems very confused at multiple levels. However it is not my job to explain general relativity. I note, though, that Milne didn't accept GR, whereas all models of inflation work within this paradigm. Application of Milne to inflation is therefore original research and expressly forbidden in Wikipedia. Good luck writing your article on the subject (and I'm not being sarcastic), but don't think it has any relevance here. --Michael C. Price ^talk 17:37, 10 August 2006 (UTC)Reply

Penrose Criticism and the entropy "problem"

Latest comment: 19 years ago46 comments5 people in discussion

Can someone explain the statement:

In [Penrose]'s opinion the biggest mystery of the Big Bang is why the universe started in a state of very low entropy. Rather than solving this problem, the inflation theory further aggravates it--the thermalization at the beginning of the inflation era pushes the initial entropy even lower--essentially requring the universe to start in a more ordered state.

Surely inflation reduces any "entropy problem"? If we require consistency with observations then the pre-inflationary region of the universe required to be in a low-entropy state is much smaller than the size of the initial low-entropy region required in a non-inflationary theory. --Michael C. Price ^talk 00:07, 4 September 2006 (UTC)Reply

Penrose seems to have problems not only with Cosmic inflation but also string theories and quantum mechanics in general (see this article). He seems to be a mathematician who by working for one field of physics (cosmology) became known as a "mathematical physicist", whatever that means. I belive his physics intuition is not much higher than the average for matematicians (that is pretty low). In general, I've seen many old scientists disbelieving any new theory they hear about.

Now, more to the point. The criticim Penrose narrates in his book is not originally his own. It comes from a paper D.N. Page, 1983, "Inflation doesn not explain time asymmetry" Nature, 304, 39 (actually a reply to an article by P.C.W. Davies, 1983, "Inflation and time asymmetry in the Universe", Nature, 301, 398). The reply to the criticism (P.C.W. Davies, 1984, "Inflation to the universe and time asymmetry", Nature, 312, 524) is actually accepting the premise that the initial state of the visible Universe (originally a microscopic amount of space before the inflation) had to have a very low entropy due to random quantum fluctuations to account for the observed thermodynamic arrow of time. However this is not a problem but a bonus for the inflation theory. The fact that the small fragment of space from which our Universe grew had to be extremely orderly to allow inflation can makes it unnecessary to make any ad-hoc theories about the initial entropy state which are necessary in other theories.

The fact that Penrose still clings to the argument (in my opinion successfully refuted) of Page after 20 years, does not make him a cutting edge criticist of the Cosmic inflation. I believe the article section should be reworked giving their due to Page and Davis for proposing this line of critique and for refuting it. Friendly Neighbour 06:34, 4 September 2006 (UTC)Reply

Perhaps we should create an entropy problem article, along the lines of the flatness problem and monopole problem? The Penrose's objection can be demolished there.--Michael C. Price ^talk 09:07, 4 September 2006 (UTC)Reply

I reworked the section, adding the original author of the critique and its rebuttal. Also, I removed the fractal sentences. Who else, besides Penrose, expects the Universe to be a fractal? Especially as in the Planck scale of length it must be more or less discrete. Friendly Neighbour 12:28, 4 September 2006 (UTC)Reply

There is no a priori reason why the universe couldn't start in a fractal state. I thing physicists have a bias towards smooth things--(piece-wise-) continuous functions, smooth manifolds, etc. Why should nature be like this? I think one should provide a good argument why the initial state should not be fractal. I'm speculating that in some sense non-fractals form a measure-zero subset of "all sets." I can see why Penrose, being a mathematician, may have a totally different perspective on things.-- Bartosz 02:54, 6 September 2006 (UTC)Reply

I see no way the Universe may have (now or in the begining) a fractal state if you cannot have any structures smaller than the Planck length. Fractals are impossible if you are length scale limited. It seems Penrose (whose idea this is) really does not believe in quantum mechanics. Friendly Neighbour 09:19, 6 September 2006 (UTC)Reply

This is a circular argument. The only rationale against structures smaller than the Planck length that I know of are based on the assumption that the current theories are still valid at such distances--which we know they aren't. Am I wrong?-- Bartosz 21:05, 6 September 2006 (UTC)Reply

Still, the burden of proof in on those who say the known laws of physics (especially Heisenberg uncertainty principle) are not valid at the Planck length scale. Otherwise, you could as well say that I use a circular argument doubting that that the Universe at the Planck scale is inhabited by garden gnomes. The only rationale against Planck gnomes is based -- according to your rationale -- on the assumption that known laws of physics hold at the distance. Friendly Neighbour 06:00, 7 September 2006 (UTC)Reply

How does Heisenberg uncertainty principle preclude structures below Planck scale? It precludes mesuring them (for instance, by Planck gnomes), but not their existence (whatever we mean by "existence" at such extreme conditions where no measurements are even imaginable) . After enough stretching by inflation, these structures could have become measurable. -- Bartosz 19:52, 7 September 2006 (UTC)Reply

The same way it limits the diameter of a proton, atom nucleus or the minimal size of electon orbits. It's a popular misconception that a measurement is needed for the Heisenberg uncertainty principle to start working. Actually, the article on the principle explains the misconception in the section titled "Common incorrect explanation of the uncertainty principle". This is actually one of the fundaments of quantum mechanics. See for example "Common Misconceptions Regarding Quantum Mechanics" by Daniel F. Styer, especially sections III.8 & III.9. Friendly Neighbour 20:10, 7 September 2006 (UTC)Reply

I am not arguing for the hidden variable interpretation, which is being alluded to in the article you're quoting. I just don't know of any physical argument that would eliminate wave functions whose wavelength is shorter than the Planck scale. -- Bartosz 18:22, 8 September 2006 (UTC)Reply

You said that Heisenberg uncertainty concerns measuring, not existence - and this is exactly the same thing as stating that hidden parameters do exist. Let's stop this nonsense. Planck length is the lower limit of meaningful physics due to this very uncertainty. If a particle is smaller than the length, it has enough momentum (and hence energy) to create virtual black holes. Its energy uncertainty is larger than its rest mass and this makes the concept of particle unclear. This i what make the concept of string (in place of point particles) so compelling. I'll stop responding here leaving you with a whole article on the subject: arXiv:9403008 {{arxiv}}: Check arxiv value (help). Friendly Neighbour 20:00, 8 September 2006 (UTC)Reply

The article predictably speaks about measurements. From the abstract: "The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity." Obviously no measurements were possible during the inflationary era. So to me your argument sounds like this: In the pre-inflationary universe one could not make any measurements that would involve scales smaller than the Planck scale; therefore, when one makes measurements now, one cannot measure traces of any structures that would correspond to sub-Planck scales back then. I just don't see the connection. I think it's more a matter of intuition than strict science, so we are probably stuck until a better theory arrives.-- Bartosz 00:52, 9 September 2006 (UTC)Reply

The fractal claim was bizarre and best removed. However I'm having problems understanding both the problem as described by Page/Penrose and Davies' rebuttal:

I don't understand the Page/Penrose clause "thermalization at the beginning of the inflation era pushes the initial entropy even lower". Perhaps this could be explained a bit more clearly / less concisely?

In the Davies rebuttal what does "a very low entropy value -- due to random quantum fluctuations -- to account for the observed thermodynamic arrow of time" mean? That the "random quantum fluctuations" drove down the entropy ? Most unlikely. Or that the entropy had to be low to "eliminate" the field fluctuations which would otherwise prevent inflation from starting? More likely. But then Davies' argument is a purely anthropic one. Surely we can do better than this? I'd reword it myself but the Davies ref doesn't appear to be available online so I can't see if this was what he meant. --Michael C. Price ^talk 10:28, 5 September 2006 (UTC)Reply

I copy-edited the section to accomodate some of the comments (the middle paragraph above). The sentence about thermaliazation was not mine - it was written by the original author of the section (User:Bartosz). I hope it is now easier to understand. I also corrected the moment of thermalization (reheating) which in fact had to happen at the end of the inflation, not in its initial stage. I'll change the word to reheating in my next edit. Friendly Neighbour 11:56, 5 September 2006 (UTC)Reply

Now, on the random fluctuation sentence. You have a point here. I used a rendition of his argument from Albrecht & Sorbo 2004: "The position we take here (which was suggested by Davies [...]) is basic acceptance of this point. If you can regard the big bang as a fluctuation in a larger system it must be an exceedingly rare one to account for the observed thermodynamic arrow of time. Also, we believe that this is the most attractive possibility for a theory of initial conditions. Other theories of initial conditions seem to us more ad hoc, and less compelling.". This is a purely anthropic idea. I have access to the Davies paper as well. Re-reading it now I'm not sure that Davies was basing his argument on the principle only. More on that soon. Friendly Neighbour 12:33, 5 September 2006 (UTC)Reply

OK, I've re-read Davies 1984. The first time was really cursory and it seemed to confirm what I read in Albrecht & Sorbo 2004. Therefore I chose the text from the latter article as the idea was more compacted and focused in their short rendering. The original Davies article considers two scenarios of inflation origin which seemed feasible at the time. One is tunneling from "nothing" in which case "inflation merely acts to drastically reduce the improbability of such a state by permitting a wide class of initial staes to develop into something like the universe we now see". The other scenario involves inflation which starts from a fluctuation of a "pre-existing Friedman-like phase". In this case "one can accept an arbitrary initial state but appeal to anthropic selection of an atypical region". This is the case Albrecht and Sorbo talked about, most probably because tunneling from nothing isn't now as popular as was in 1984.

I'll add that a quantum fluctuation can easily decrease locally entropy. Entropy grows only globally. For example, we are living examples of local entropy decrease. Of course, the world pays an entropy price for our existence. Friendly Neighbour 13:29, 5 September 2006 (UTC)Reply

Albrecht & Sorbo 2004 is a great link that you gave. Indeed I suggest replacing Davies' argument altogther with Albrecht & Sorbo's. Howabout:

In fact the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelming favours the inflationary scenario[4], simply because the amount of "seed" required for the inflationary cosmos is so much less than any non-inflationary alternative.

What do you think? --Michael C. Price ^talk 17:44, 5 September 2006 (UTC)Reply

I definitely like it. Fire when ready ;-) Friendly Neighbour 19:11, 5 September 2006 (UTC)Reply

Great, I see you've found a "proper" ref for it. --Michael C. Price ^talk 19:55, 5 September 2006 (UTC)Reply

This whole field is widely speculative, so I don't think one should use statements that suggest some kind of strictness of argument.

"In fact the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state, compared with a non-inflationary cosmos overwhelming favours the inflationary scenario, simply because the amount of "seed" required for the inflationary cosmos is so much less than any non-inflationary alternative."

One can talk of probability only within a certain framework that defines the space of possibilities. We have no agreed framework for eveluating pre-big-bang states. What "seed" are we talking about and how do we measure its amount?

I suggest you download the PDF article for these details. --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)Reply

If nobody protests, I'll remove this sentence.

My understanding of the original criticism of inflation is that it tries to solve what is perceived as a problem by exaggerating another problem. Why do two remote regions of the universe have the same temperature? It could be because they started at the same temperature, or because they had time to exchange heat. Inflation is based on the premise that it is unreasonable for the universe to start in a uniform state, therefore there had to be a thermalization period. But the non-uniform state has lower entropy than the uniform state. One might say that it's even more unreasonable to assume such low entropy for the initial state. I'm not saying I buy that argument, but I see the point.

Bartosz 23:53, 5 September 2006 (UTC)Reply

This isn't quite a fair shake for the theory. Inflation developed with the understanding that the horizon problem was difficult to resolve using "standard" cosmology, but Linde wasn't looking for a patchwork for this. It just happens that a scalar field inflates. There really is nothing more to it than that. Highly symmetrical universes inflate as a general rule: the theoretical exception are those models which do not have a kind of inflation. To this end, inflation is not a cart-before-the-horse proposition at all, it is a fully "organic" result of the simplification of physics at high densities and pressures. --ScienceApologist 00:14, 6 September 2006 (UTC)Reply

I'm not sure which is cart and which is horse. Universes with a cosmological constant inflate, but they never stop. Scalar fields and phase transitions are still very speculative (meaning, we haven't seen a Higgs yet, and there is no accepted GUT). So present-day particle physics offers little support for inflation. In general, I'm a little worried about the whole article giving the wrong impression to non-specialists about what is solid science and what is speculation. According to Penrose, physics before 10^-1s after the Big Bang is speculative and I think this is a good ballpark. -- Bartosz 01:47, 6 September 2006 (UTC)Reply

The article clearly states that the particles physics is speculative. However the astrophysical reasoning is quite sound. Inflation is now understood as a generic property of various theories (indeed most theories) and is not arm-waving. --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)Reply

Penrose, in the best tradition of skittish scientists, is being overly conservative with his characterizations and ignores/is unaware of the astrophysical evidence. WMAP, after all, has firmly established an inflationary universe in a very clever way. It's a bit arbitrary for Penrose to make a 10^-1s cut-off for parameterizing ignorance. Obviously he's more comfortable with nucleosynthesis than he is with baryogenesis, but this may be due to sour grapes since his early universe theories fell rather flat. In particular, the detail parameterization of inflation is well-understood from the observational evidence and the generic quality of inflationary models (it doesn't matter what kind of GUT is correct, it just matters that the physics follows the currently observed trend of becoming more and more symmetrical at higher energies). ScienceApologist 12:28, 6 September 2006 (UTC)Reply

Friendly Neighbour says: "I also corrected the moment of thermalization (reheating) which in fact had to happen at the end of the inflation, not in its initial stage. I'll change the word to reheating in my next edit."

I may be wrong, but my understanding is that the thermalization happened at the beginning and not at the end of inflation (also, it is not the same as "reheating"). In an exponentially expanding universe, the distances between points increased very slowly at the beginning, then accellerated very rapidly (an exponential curve always starts slowly). Heat exchange could only take place in the slow phase. Compare it with the non-inflationary solutions, where the expansion is the fastest at the beginning, precluding any exchange of heat. —The preceding unsigned comment was added by Bartosz (talk • contribs) .

You are wrong, thermalisation occurs at the end of inflation, when the inflaton field decays into an array of other particles. Whilst inflation is in progress this decay (and the associated temperature rise) is supressed. That's why it is called "reheating". --Michael C. Price ^talk 07:00, 6 September 2006 (UTC)Reply

I think that Bartosz was talking about equilibration which is a generic property of inflating regions -- but it doesn't just deal with temperature -- EVERYTHING equilibrates. During inflation, temperature is an ill-defined measurement, that's why reheating is so interesting. --ScienceApologist 12:32, 6 September 2006 (UTC)Reply

Well, he used the term "thermalization". Friendly Neighbour 12:41, 6 September 2006 (UTC)Reply

My understanding is that exponential expansion started off slowly, so the whole region that later became the visible universe, had enough time to reach thermal equilibrium. At the end of the inflation, this region was already too big and expanding too fast to allow for heat transfer between its far ends. -- Bartosz 19:52, 7 September 2006 (UTC)Reply

Inflation does have its problems (as any new theory is expected to have). They are nicely resumed in Brandenberger 2001 (linked also from the article page). Arrow of time is not even mentioned there as it is a recent rehash of an old argument from 1980s (see above for details). Therefore, we should either beef up the Criticism section (renaming it to something like "Problems of Cosmic Inflation") or maybe delete it completely as it now focuses only on an obscure argument about something which is not even a central concept of the theory (and IMHO the arrow of time discussion is anyway more in the realm of philosophy than physics, anyway). What do you think? Friendly Neighbour 09:04, 6 September 2006 (UTC)Reply

It is not an obscure argument in the public / pop' science ___domain -- I've seen it referred to in various forms in the last decade (usually citing Penrose as source) -- so it definitely has a place here. (I don't agree that the arrow of time is a philosophical issue -- although most philosophers lack sufficient grounding in thermodynamics to be able to discuss it with any competence.) As for what to do with the criticism section, I agree: either more problems should be included (e.g. lack of firm Higgs data) or the title changed. --Michael C. Price ^talk 11:11, 6 September 2006 (UTC)Reply

Arrow of time question in Cosmic inflation

Caveat: this opinion of mine is an off-topic philosopical opinion and does not cover to the question of what to do with the section:

I knew someone will react :-) But I'm quite serious. If you think for example about the demarcation criterion proposed by Karl Popper, what possible machanism of falsifying the connection of the arrow of time with entropy can one offer? Even as I am not quite a fan of Popper, I see a problem here. If there is no way (and by possible I don't mean technically feasible but not breaking any laws of logic and physics ruling our Universe) of testing a hypothesis, then it is not physics. It's philosophy. (I'm not sure whether Popper was aware that philosophy is not science according to his own solution of the demarcation problem but it obviously isn't). Friendly Neighbour 12:07, 6 September 2006 (UTC)Reply

Thermodynamics has a lot of overlap with information theory, the latter which has theorems which are tautologically provable rather then empirically provable. I suspect that the thermodynamics / arrow of time issue lies within this tautological ___domain. --Michael C. Price ^talk 14:25, 6 September 2006 (UTC)Reply

We go a looong way off-topic here but I can't resist replying ;-) I do not agree that thermodynamics is not experimentally testable. You test it every time you start the engine in your car. You test it every time you have to heat the water to boil it instead of waiting until decreasing entropy does it spontaneously. Etc. etc. It's the thermodynamics <-> time arrow conection which is, in my opinion, physically non-testable. Simply because thermodymanics has the only law we know that is not time reversible (except for the charge-parity symmetry which is somehow a less popular "source" of the arrow of time), people connect the two together. In fact there is no evidence that CP symmetry, some yet unknown law of physics or even nothing at all is the reason time goes in the direction we observe (if it does at all). I'll have yet to finish "The Fabric of the Cosmos: Space, Time, and the Texture of Reality" by Brian Greene but I doubt that even he can convince me about the importance of the connection. Friendly Neighbour 14:58, 6 September 2006 (UTC)Reply

Just to correct a missimpression I seem to have made - not all thermodynamics is tautological (I think we agree on this): just the overlap with information theory.

It's a fun subject, and not entirely off-topic, since inflation - arguably - is the "source" of the universe's free-energy. I remember attending a talk by Davies c1981 where he argued precisely this point. I say "precisely", although I have forgotten the details :-( ; something to do with inflation creating the gap between the universe's actual entropy and the maximum possible entropy. But the talk included the claim that inflation had finally "explained" the arrow of time. I'll have to dig around and see if he wrote anything on the subject. --Michael C. Price ^talk 16:21, 6 September 2006 (UTC)Reply

I'll also read today, if time allows, (pun intended) the paper (Milan M. Cirkovic "The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument", Foundations of Physics, 33, 3, March 2003) whose author claims in the abstract that he showed "that there is a third possible alternative, based on the generalization of the classical (‘‘Boltzmann–Schuetz’’) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann’s statistical measure at its face value, and accomodating it within the quantum cosmological concept of the multiverse. ". But that's exactly what I was afraid of. You have to create a Multiverse to test experimentally the concept ;-) Friendly Neighbour 16:43, 6 September 2006 (UTC)Reply

OK, Cirkovic thinks he invented the anthropic Multiverse reason of growing entropy (life is possible only in universes where it increases). In fact Davies in his 1984 article used it, though not as expliciotely. I'm still not sure why people think that explaining the growing entropy explains also the direction of time.

By the way, Hawking had a hillarious paper on the subject (Hawking, 1985, "Arrow of time in cosmology", Phys. Rev. D 32, 10, 2489-2495). He thought that in a collapsing universe or close to a black hole the entropy would fall. He even proposed an experimental test involving a black hole! However, in a long note added after the review he thanks Don Page for showing that the expected entropy decrease is not true. Hawking still saw two points of his paper that remained correct. The second one (that a universe started with inflation will have a well defined arrow of time!) is never mentioned in the article itself. How bizarre. I wonder why he didn't retract the whole thing. Friendly Neighbour 19:00, 6 September 2006 (UTC)Reply

Is that the same paper where Hawking predicts that time will flow backward when/if the universe starts to contract? A real clanger!

Well, he was cautious enough to use the term "thermodynamical arrow of time" everywhere in the article, defining it as "the direction of time in which entropy increases". Therefore I read his contracting universe prediction simply as "entropy will decrease" (I cannot grasp the alledged reason why time flow will follow entropy) and some people understand it as "time will reverse" which is not necessary the same. Friendly Neighbour 19:58, 6 September 2006 (UTC)Reply

I guess the reason why people think that the entropy gradient defines the arrow of time is that we have the Planck-Boltzmann law ${\displaystyle S=k\log \Omega }$ . Number of microstates ${\displaystyle \Omega }$  correlates with the entropy S. Thus we can define a one-to-many relationship between the macrostates in the past with the macrostates in the future, by the appropriate grouping or microsates into macrostates. Hence we can remember the past because we can define a unique macrostate for it, but there is too much choice for the future. There are many other ways of expressing this of course. --Michael C. Price ^talk 19:38, 6 September 2006 (UTC)Reply

I have a gut feeling that this is exactly where philosophy starts. Friendly Neighbour 19:58, 6 September 2006 (UTC)Reply

I feel the same way about anthropic based arguments. --Michael C. Price ^talk 20:22, 6 September 2006 (UTC)Reply

Generally, from what I read today there are three explanations of the "thermodynamic arrow of time":

• statistical laws say so - the entropy must grow (for me the most sound, for most persons involved a lame argument),
• initial conditions of low entropy - for accident by a random quantum fluctuation before the inflation (inflation does make it much easier to imagine this "accident"),
• the anthropic principle - in fact a variant of the second argument, just adding the fact that otherwise we would not live to observe the universe.

I do not like the anthropic principle too much. For me the first explanation is good enough. if, not inflation makes me easier to imagine the random fluctuation that created our freak universe. But some people prefer to think in the anthropic way. So be it. Friendly Neighbour 20:42, 6 September 2006 (UTC)Reply

For me the statistical argument is weak because the same logic that dictates that ${\displaystyle S(t_{n+1})\geq S(t_{n})}$  also implies ${\displaystyle S(t_{n-1})\geq S(t_{n})}$ . So, if we don't like the anthropic principle, we are left with only the initial conditions argument. --Michael C. Price ^talk 00:18, 7 September 2006 (UTC)Reply

For a not so philosophical attempt you may want to read hep-th/0301115 by Detlev Buchholz. --Pjacobi 20:11, 6 September 2006 (UTC)Reply

Thanks for adding one more arrow of time. A "relativistic quantum timelike cone arrow of time"? Friendly Neighbour 20:42, 6 September 2006 (UTC)Reply

Edits by User:Bhenderson

Latest comment: 19 years ago1 comment1 person in discussion

A new user continues to make edits to this page that are slightly problematic. The prose he includes doesn't add any substantive information to the article and introduce a misconcpetion that inflation accounts for the current scale of the universe (which it doesn't because expansion is still occuring). --ScienceApologist 15:57, 10 September 2006 (UTC)Reply

Some more sources on cosmic inflation and the arrow of time

Latest comment: 19 years ago1 comment1 person in discussion

I've found some more sources we could use:

1. Sean M. Carroll, Jennifer Chen, 2004 "Spontaneous Inflation and the Origin of the Arrow of Time", hep-th/0410270
2. Sean M. Carroll, Jennifer Chen, 2005, "Does Inflation Provide Natural Initial Conditions for the Universe?", gr-qc/0505037
3. Robert M. Wald, 2005, "The Arrow of Time and the Initial Conditions of the Universe", gr-qc/0507094

The first two papers claim to have explained why "spontaneous eternal inflation can provide a natural explanation for the thermodynamic arrow of time" and why "a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time". The third paper argues that "it is not plausible that these special initial conditions have a dynamical origin" or to put it plainly does not believe that inflation explains why the universe had to start in a low entropy state. Friendly Neighbour 18:30, 27 September 2006 (UTC)Reply

Questions and edits regarding usage of Inflaton in first pararagraph

Latest comment: 19 years ago2 comments2 people in discussion

I recently made an edit to the sentence in the first paragraph, to generalize usage of the term Inflaton, which made it more closely reflect Wikipedia's entry. I also inserted the word believed (possibly mis-spelled), and it was recently deleted. Is there a clear consensus with this body of editors, regarding whether the Scalar field (or constant B-field) referred to as the Inflaton is regarded as a fact? I thought that; at this point it is considered an abstraction which is convenient in String Theory and M-Theory, to account for the observed properties of Cosmic Inflation. I would like to state that there are some perfectly reasonable Inflationary Universe theories currently being considered, which do not employ the Inflaton. It seems a bit gratuitous to present it as a fact, therefore. JonathanD 16:42, 12 October 2006 (UTC)Reply

Well, the scalar field has been the standard way to discuss inflation since Guth. So it is a pretty accepted part of inflation theory – which is not to say that if inflation ultimately turns out to be correct, it has to be governed by a scalar field, because inflation only means a short, de Sitter-like epoch in the early universe. There are a few attempts at inflation without additional scalar fields, namely Starobinsky's early work suggesting that inflation arose in the early universe from quantum corrections to gravity, and Dirac-Born-Infeld inflation in string theory, in which the role of the inflaton is played by the position of a D-brane (which can be thought of as a scalar field, but not simply). But I would say that having a scalar inflaton is much less controversial than inflation itself.

As for how widely inflation is believed, well, the predictions of inflation have been very accurately confirmed, so any successor will have to make the same predictions. On the other hand, the theory itself is on somewhat shaky ground. I think most people believe that the basic picture works, but that the theory might still have some surprises in store. –Joke 19:48, 12 October 2006 (UTC)Reply

Is there not also "vector inflation" where the inflaton is not a scalar field but a -- surprise, surprise -- vector field, without recourse to string theory or quantum gravity?

How long?

Latest comment: 19 years ago45 comments4 people in discussion

The overview states:

"It is not known how long inflation lasted but it is thought to be extremely short. "

But what about the possibility of eternal inflation? --Michael C. Price ^talk 08:51, 13 October 2006 (UTC)Reply

I changed the wording of this slightly. Although inflation didn't happen for very long in terms of today's timescales, it lasted for many Hubble times and therefore was a pretty long event in the grand scheme of things up until that point. Since eternal inflation depends on higher potential false vacuums, I think we can safely assume we are talking about the latest round of vacuum decay rather than the infinite regression of vacuum decays that may or may have not happened in the past. --ScienceApologist 01:04, 15 October 2006 (UTC)Reply

It still doesn't address the eternal inflation possibility which, AFAIK, does not depend exclusively "on higher potential false vacuums". Until the nature of the inflaton is discerned we should be open to the possibilty that the latest round of inflation may have been both chaotic and eternal -- i.e. of indefinite duration. --Michael C. Price ^talk 08:19, 15 October 2006 (UTC)Reply

Even if it is eternal to both the past and future, it is still possible that any given worldline is finite and of short duration (compared to, say, a second). I think this is what actually happens, but can't say for sure (and even if I could that would be OR). So while inflation is eternal, a worldline chosen at random has a finite expected proper length. This is like how in probability theory an unbounded positive random variable can still have finite expectation value.

On a broader note, this is a common statement in the popular and technical literature. It can be interpreted most simply to mean that the last sixty e-folds last a very short time. –Joke 01:20, 16 October 2006 (UTC)Reply

For a world line starting during eternal inflation and going forward in time the proper inflationary time would be short time, but what about a world line projected back in time? Wouldn't that be of indefinite duration? --Michael C. Price ^talk 06:52, 16 October 2006 (UTC)Reply

I was basing my comments on the comment above from an IP anon:

Dr. Linde does discuss in this paper his opinion that even though any particular past-directed geodesic must have finite length, there is no reason to conclude that there must be an upper limit on that length, so inflation can be eternal in the past.

So according to this statement, every past-directed geodesic ends eventually. I really don't know what to say beyond this – I had thought that the Borde-Guth-Vilenkin argument was universally accepted until I saw this discussion. –Joke 01:59, 17 October 2006 (UTC)Reply

Yes, according to that statement every past-directed geodesic ends eventually -- but that is precisely what we are not discussing . We are discussing whether it must end within any particular definite period -- and the answer is that it need not. --Michael C. Price ^talk 02:18, 17 October 2006 (UTC)Reply

Well, it's a bit of a stretch to say that it is precisely what we were not discussing. Of course the length of a worldline can be unbounded (in future-eternal inflation that is true too). But still, a typical worldline has a very short proper length (again, compared to say, one second). –Joke 02:38, 17 October 2006 (UTC)Reply

With eternal inflation a typical worldline has a short future proper length but an unbounded proper length to the past. --Michael C. Price ^talk 09:01, 17 October 2006 (UTC)Reply

Hmm, perhaps this can all be resolved if we state that the inflationary epoch lasted on the order of 10^-30 seconds (being 100s if not 1000s of times more generous), but that it lasted for many Hubble times. After all, it's the inflationary epoch that people usually describe as "inflation". Chaotic/eternal inflation involves other inflationary epochs that occur at other earlier/later times.

How do we know that the lastest, and perhaps only, period of inflation wasn't chaotic/eternal? --Michael C. Price ^talk 14:01, 17 October 2006 (UTC)Reply

Depends on whether you think the Hubble parameter was bounded or not. Most inflationary models require it to be constant. If this is true than inflation has a beginning and an end. Models that include a changing Hubble parameter are still bound by the peculiar effect that the flatness of inflation chooses a lower-bound for the Hubble parameter. In effect, an inflating solution to the Einstein equations prevents eternal past-worldlines from existing in our universe because when you assume they exist they simply do not show up for similar reasons that there are no point defects. I have yet to see a contradiction to this.--ScienceApologist 07:30, 18 October 2006 (UTC)Reply

I don't understand the "point defects" reference. Could you explain more? Do you refer to the Borde-Guth-Vilenkin singularity argument? --Michael C. Price ^talk 07:59, 18 October 2006 (UTC)Reply

Yes, and more. A bounded Hubble parameter implies that inflation had to "start" for most worldlines. Vilenkin wrote a number of papers about this. --71.57.90.3 00:54, 20 October 2006 (UTC)Reply

Which have been superseded by past eternal inflationary models which are singularity free and geodesically complete:^[1][2]. --Michael C. Price ^talk 06:22, 20 October 2006 (UTC)Reply

However, in both of these papers, the question that's being asked isn't "are all worldlines infinite?" but rather "does there exist an infinite worldline?" These articles do not supercede the general point that point defects reign supreme as you go back to conformal times where the universe is less inflated. --ScienceApologist 12:35, 20 October 2006 (UTC)Reply

No, the main question being asked "Have we circumvented the restrictions implied by "Borde Guth Vilenkin", which they reference, and the answer is yes. They have constructed a steady state, past and future eternal inflationary scenario. --Michael C. Price ^talk 12:43, 20 October 2006 (UTC)Reply

Not clear that the answer is as baldly "yes" as you are claiming it to be. In fact, these papers admit that their volumes that contain bundles of infinite worldlines asymptotically approach zero for the total universe. While they also propose some cosmetic fixes for this problem, what we ultimately have is BGV coming back to haunt the authors as they try to avoid it. --ScienceApologist 13:21, 20 October 2006 (UTC)Reply

No, it is quite simple. The BGV worldlines from "I" simply cross over into "II", and vice versa. --Michael C. Price ^talk 14:14, 20 October 2006 (UTC)Reply

That's the idea, but there is no attempt to describe how many worldlines actually end up in I in the first place. But that's okay because they didn't set out to prove this as a statistical argument: only a possibility argument (as I've been stating all along). --ScienceApologist 18:35, 20 October 2006 (UTC)Reply

I disagree with your original research, but it's irrelevant anyway: the possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. --Michael C. Price ^talk 02:39, 21 October 2006 (UTC)Reply

As I've been saying all along, there is no contradiction in something having unbounded length to the past but having the expected length short. Certainly the length to the future is unbounded (but also has quite short expected length) in any eternal inflation scenario. –Joke 13:34, 17 October 2006 (UTC)Reply

Just because there's no contradiction with your statement doesn't mean it's either true or appropriate for the article. There are too many theories about inflation, with insufficient empirical grounding to distinguish amongst them, to state that the period of inflation was "short". All we can say is that is there is a minimum period/amount of inflation required to resolve various astrophysical conundrums. --Michael C. Price ^talk 14:01, 17 October 2006 (UTC)Reply

OK, fine, but all existing theories of inflation have inflation last a short period. The Hubble time is essentially the only physical parameter during inflation, and it sets the timescale. Inflation lasts many Hubble times, but even if it lasts a billion Hubble times, it is still short. Yesterday I changed the phrasing to "usually thought to be extremely short compared to today's timescales" which is so equivocal that surely everybody can be satisfied? –Joke 14:29, 17 October 2006 (UTC)Reply

The wording is better, but I'm still having problems reconciling the use of "short" with "unbounded". At the very least the article looks inconsistent, saying that the period of inflation is thought to be short and then discussing eternal inflation: "New inflation is generally eternal: that is, the process continues forever." BTW my previous question "How do we know that the lastest, and perhaps only, period of inflation wasn't chaotic/eternal? " remains unanswered. --Michael C. Price ^talk 15:00, 17 October 2006 (UTC)Reply

Current expectation is that it is both chaotic and eternal. Here is the picture: take an ensemble of worldlines in an eternally inflating universe. The end of inflation occurs somewhat like radioactive decay: it has an exponential distribution with finite expected time τ until the end of inflation. So inflation has ended on about half (really 1-1/e) of the worldlines after time τ. However, the space around the remaining worldlines has expanded so dramatically that you can't really say that less of the universe is inflating. It is the weird paradox of eternal inflation: any given observer (such as ourselves) experiences inflation for only a short time, while the universe as a whole inflates indefinitely. It is another one of these strange problems of gravitational gauge fixing, Bayesian proability and the anthropic principle and has been causing people a lot of grief defining anything sensible in the string landscape, for example. –Joke 15:53, 17 October 2006 (UTC)Reply

That's fine, I have no problem with that explanation. It explains why a typical observer would expect inflation to end within a short period, but it does not explain, or give any reason to expect, the past of the same world line(s) would have experienced inflation for a similarly brief period. --Michael C. Price ^talk 18:00, 17 October 2006 (UTC)Reply

What you are arguing is essentially akin to arguing that it is possible to win the lottery and prove the Second Law of Thermodynamics incorrect. While technically the statistics don't forbid you from having a worldline that is eternal, the probability of such a thing is so vanishingly small as to be as impossible as seeing a glass spontaneously reassemble by having every particle tunnel into the appropriate arrangement. Just not going to happen. --ScienceApologist 07:36, 18 October 2006 (UTC)Reply

No, eternal inflation forms a tree-like (almost fractal) structure with the branches pointing forward in time. A typical worldline terminates quite soon (for the reason given by the radioactive decay analogy). But tracing the same worldlines backwards simply moves to older sections of the trunk. --Michael C. Price ^talk 07:52, 18 October 2006 (UTC)Reply

Let's try another tack, and call the moment when eternal/chaotic inflation kicks off t=0. What is the expected value of t (i.e. the period of past inflation) for a typical observer? t is larger than any finite value, since there is more(*) "volume" (inflating and post-inflating) to the future than to the past of any space-like hypersurface. (*"More" because there is only a finite amount to the past, an unbounded, infinite amount to the future.) Ergo the expected duration of past eternal inflation is infinite -- or at least very, very large, probably unbounded and certainly not "short" by any stretch of the imagination, by any Bayesian computation.

PS this picture does not conflict with the second law of thermodynamics since entropy is always increasing with time. --Michael C. Price ^talk 10:41, 18 October 2006 (UTC)Reply

You're missing the point of the analogy. It's not to say that your view violated the second law of thermodynamics; it's to say that your counter-example to brief inflation is so entirely unlikely as to be impossible. --71.57.90.3 00:50, 20 October 2006 (UTC)Reply

And you're missing the point that references already in the article support past eternal inflation^[3][4].

No, I'm pretty sure I understand what they are saying. There doesn't seem to be a contradiction in stating that a single worldline may be infinite but may also be impossible to find. --ScienceApologist 12:35, 20 October 2006 (UTC)Reply

No, all geodesic wordlines are proper time infinite in their construction. They would hardly call it steady state, past eternal inflation otherwise -- and not just in passing but all the way through both articles. Look at the conformal diagrams. --Michael C. Price ^talk 12:40, 20 October 2006 (UTC)Reply

Here's one of the abstracts. It's pretty unambiguous:

Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a "steady-state" model with no initial time. Here we provide a construction that circumvents these theorems and allows a self-consistent, geodesically complete, and physically sensible steady-state eternally inflating universe, based on the flat slicing of de Sitter space. This construction could be used as the background space-time for creation events that form big-bang-like regions, and hence could form the basis for a cosmology that is compatible with observations and yet which avoids an initial singularity or beginning of time.

--Michael C. Price ^talk 12:52, 20 October 2006 (UTC)Reply

I just reread the papers. The construction they are talking about in the paper you cite is essentially arguing that in their unique form of double-well inflation, the global symmetries of inflating spacetime admit some geodesics that are infinite (highlighted in their conformal diagrams). This I don't argue with, but BGV never said anything about there not being any infinite geodesics, it said (essentially) that the probability of finding such a geodesic is zero given the eternal nature of inflation. The authors are careful to avoid saying that they disproved BGV, but instead argue that their construction has the possibility to avoid singularities. However, they don't give any indication of how likely it is to do this and are clear that there are worldlines in their models which do not have this feature. --ScienceApologist 13:21, 20 October 2006 (UTC)Reply

Their models are not dependent on their "unique form of double-well inflation", but would appear in any eternal inflation model --- which is most of forms inflation we are interested in. As for how probable their model is -- well that is speculative, of course, as are all models of inflation.--Michael C. Price ^talk 14:18, 20 October 2006 (UTC)Reply

The relevant point to note is that the beginning of inflation in the model is infinitely in the past of the typical observer (${\displaystyle t=-\infty }$  in their diagrams). Hence claiming that inflation in our past was "short" is not correct. --Michael C. Price ^talk 14:43, 20 October 2006 (UTC)Reply

No, they make no claims on the "typical" observer. They make claims on the existence of an observer who sees such a thing. But that observer has to be in a special part of their model: a part that is emphasized by their choice of conformal diagram, but isn't rigorously shown to be the most probable worldline. And they admit that there are worldlines in their model which are not infinite so the point I'm making stands. --ScienceApologist 18:35, 20 October 2006 (UTC)Reply

Again, I disagree with your original research (they do mention the randomly choosen observer in the context of the PCP which they claim is adhered to in their model), but it's irrelevant anyway: the possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. That statment only applied to the original "old" and "new" inflation which predates the chaotic eternal models. --Michael C. Price ^talk 02:39, 21 October 2006 (UTC)Reply

My understanding is that it would be exactly the same thing going into the past, except that you would run into singularities, not reheating. –Joke 00:46, 18 October 2006 (UTC)Reply

There's no connection between the two timescales, they are simply different physical processes. Think about the radioactive analogy: the decay time of an isotope has no connection to the formation time of the same isotope. This simply so obvious that I don't what else to say. --Michael C. Price ^talk 05:56, 18 October 2006 (UTC)Reply

That's a priori true, but there is only one timescale during inflation: the Hubble time. So both the time for the end of inflation and the time for the formation of singularities must be related to it in a straightforward way. It's a simple case of dimensional analysis. –Joke 14:04, 18 October 2006 (UTC)Reply

By the same argument the universe would never be able to inflate beyond its Hubble distance -- yet it does; that's the whole point of inflation. --Michael C. Price ^talk 15:11, 18 October 2006 (UTC)Reply

No, these are rough estimates. There are other dimensionless constants, such as the slow-roll parameters (ε and η) and H/m_Pl that occur in the expressions for these dynamical timescales. But none of these constants are going to change 10^{−33 seconds to one second unless some incredible fine-tuning occurs. –Joke 15:41, 18 October 2006 (UTC)}Reply

Sorry, I must have missed the explanation of why your dimensional argument applies to the Hubble time but not the Hubble distance. Anyway this is all besides the point: a dimensional argument wouldn't prevent the inflationary past duration from being infinite (see above). --Michael C. Price ^talk 15:51, 18 October 2006 (UTC)Reply

possibility that their steady state eternal inflation model is correct is enough to refute the statement that we would expect the period of past inflation to be short. -- No it's not enough to refute the statement. It's the opinion of a single pair of researchers. Joke is right, it's "usually" considered short. --ScienceApologist 02:54, 21 October 2006 (UTC)Reply

Eternal Inflation

Latest comment: 19 years ago1 comment1 person in discussion

Two refs on the subject of eternal inflation were moved -- one of the links was incorrect. I've corrected it and restored the links (which appear twice). They seem relevant to both sections. --Michael C. Price ^talk 06:09, 18 October 2006 (UTC)Reply

1. Anthony Aguirre, Steven Gratton, Inflation without a beginning: A null boundary proposal, Phys.Rev. D67 (2003) 083515, [5]
2. Anthony Aguirre, Steven Gratton, Steady-State Eternal Inflation, Phys.Rev. D65 (2002) 083507, [6]
3. Anthony Aguirre, Steven Gratton, Inflation without a beginning: A null boundary proposal, Phys.Rev. D67 (2003) 083515, [7]
4. Anthony Aguirre, Steven Gratton, Steady-State Eternal Inflation, Phys.Rev. D65 (2002) 083507, [8]