The ΛCDM model assumes that the [[shape of the universe]] is of zero curvature (is flat) and has an undetermined topology. In 2019, interpretation of Planck data suggested that the curvature of the universe might be positive (often called "closed"), which would contradict the ΛCDM model.<ref>{{cite journal|url=https://www.nature.com/articles/s41550-019-0906-9|title=Planck evidence for a closed Universe and a possible crisis for cosmology|author1=Eleonora Di Valentino|author2=Alessandro Melchiorri|author3=Joseph Silk|journal=Nature Astronomy|volume=4|doi=10.1038/s41550-019-0906-9|arxiv=1911.02087|date=4 November 2019|issue=2|pages=196–203|s2cid=207880880|access-date=24 March 2022}}</ref><ref name="Snowmass21"/> Some authors have suggested that the Planck data detecting a positive curvature could be evidence of a local inhomogeneity in the curvature of the universe rather than the universe actually being globally a 3-[[manifold]] of positive curvature.<ref>{{cite journal|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.87.081301|title=What if Planck's Universe isn't flat?|author1=Philip Bull|author2=Marc Kamionkowski|journal=Physical Review D|volume=87|issue=3|date=15 April 2013|page=081301|doi=10.1103/PhysRevD.87.081301|arxiv=1302.1617|bibcode=2013PhRvD..87h1301B|s2cid=118437535|access-date=24 March 2022}}</ref><ref name="Snowmass21"/>
=== Violations of the strong equivalence principle ===
{{main|Strong equivalence principle}}
The ΛCDM model assumes that the [[strong equivalence principle]] is true. However, in 2020 a group of astronomers analyzed data from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample, together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. They concluded that there was highly statistically significant evidence of violations of the strong equivalence principle in weak gravitational fields in the vicinity of rotationally supported galaxies.<ref>{{Cite journal|arxiv = 2009.11525|doi = 10.3847/1538-4357/abbb96|title = Testing the Strong Equivalence Principle: Detection of the External Field Effect in Rotationally Supported Galaxies|year = 2020|last1 = Chae|first1 = Kyu-Hyun|last2 = Lelli|first2 = Federico|last3 = Desmond|first3 = Harry|last4 = McGaugh|first4 = Stacy S.|last5 = Li|first5 = Pengfei|last6 = Schombert|first6 = James M.|journal = The Astrophysical Journal|volume = 904|issue = 1|page = 51|bibcode = 2020ApJ...904...51C|s2cid = 221879077 | doi-access=free }}</ref> They observed an effect inconsistent with [[tidal force|tidal effects]] in the ΛCDM model. These results have been challenged as failing to consider inaccuracies in the rotation curves and correlations between galaxy properties and clustering strength.<ref>{{Cite journal |last1=Paranjape |first1=Aseem |last2=Sheth |first2=Ravi K |date=2022-10-04 |title=The phenomenology of the external field effect in cold dark matter models |url=https://academic.oup.com/mnras/article/517/1/130/6713954 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=517 |issue=1 |pages=130–139 |doi=10.1093/mnras/stac2689 |doi-access=free |issn=0035-8711|arxiv=2112.00026 }}</ref> and as inconsistent with similar analysis of other galaxies.<ref>{{Cite journal |last1=Freundlich |first1=Jonathan |last2=Famaey |first2=Benoit |last3=Oria |first3=Pierre-Antoine |last4=Bílek |first4=Michal |last5=Müller |first5=Oliver |last6=Ibata |first6=Rodrigo |date=2022-02-01 |title=Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies |url=https://www.aanda.org/articles/aa/abs/2022/02/aa42060-21/aa42060-21.html |journal=Astronomy & Astrophysics |language=en |volume=658 |pages=A26 |doi=10.1051/0004-6361/202142060 |issn=0004-6361 |quote=We hence do not see any evidence for a violation of the strong equivalence principle in Coma cluster UDGs, contrarily to, for instance, Chae et al. (2020, 2021), for disc galaxies in the field. Our work extends that of Bílek et al. (2019b) and Haghi et al. (2019a), which is limited to DF44 and makes the result all the more compelling. We recall that the MOND predictions do not involve any free parameter.
