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Extended models allow one or more of the "fixed" parameters above to vary, in addition to the basic six; so these models join smoothly to the basic six-parameter model in the limit that the additional parameter(s) approach the default values. For example, possible extensions of the simplest ΛCDM model allow for spatial curvature (<math>\Omega_\text{tot}</math> may be different from 1); or [[quintessence (physics)|quintessence]] rather than a [[cosmological constant]] where the [[Equation of state (cosmology)|equation of state]] of dark energy is allowed to differ from −1. Cosmic inflation predicts tensor fluctuations ([[gravitational wave]]s). Their amplitude is parameterized by the tensor-to-scalar ratio (denoted <math>r</math>), which is determined by the unknown energy scale of inflation. Other modifications allow [[hot dark matter]] in the form of [[neutrino]]s more massive than the minimal value, or a running spectral index; the latter is generally not favoured by simple cosmic inflation models.
Allowing additional variable parameter(s) will generally ''increase'' the uncertainties in the standard six parameters quoted above, and may also shift the central values slightly. The table
Some researchers have suggested that there is a running spectral index, but no statistically significant study has revealed one. Theoretical expectations suggest that the tensor-to-scalar ratio <math>r</math> should be between 0 and 0.3, and the latest results are within those limits.
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