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### [1104.1300]
Is the Universe homogeneous?

Posted: **April 08 2011**

by **Molly Swanson**

This interesting paper examines perhaps the most fundamental assumption in cosmology: homogeneity. This seemingly obvious assumption is actually quite difficult to test properly since we can only observe on our past , light cone, not on spatial slices of spacetime. The author examines in detail what observations can test for isotropy, and argues that is far from trivial to prove that the isotropy of the CMB for all observers implies homogeneity.

He also discusses tests of the Copernican Principle, which is the key to linking isotropy we observe to homogeneity. These tests include consistency of luminosity distances (testable by SNIa) and comparison of the radial and transverse BAO signals, as well as tests based on the SZ effect in clusters. In principle these tests can be done well with upcoming dark energy experiments, which I think will be a valuable complement to the traditional dark energy measurements.

### Re: [1104.1300] Is the Universe homogeneous?

Posted: **April 11 2011**

by **Syksy Rasanen**

These are not really tests of the Copernican Principle i.e. the statement that our position is not special. They are tests of the FRW approximation, i.e. to which degree the FRW model describes the real universe. Even if your position is typical, it may be that your observations are not described by a FRW model because the universe is not exactly homogeneous and isotropic.

### [1104.1300] Is the Universe homogeneous?

Posted: **April 12 2011**

by **Molly Swanson**

True, these tests are all framed as "If we observe such and such, then our universe is non-FLRW." But the idea is to combine them with independent tests of isotropy as discussed in the first half of the paper. Since isotropy+copernican principle -> FLRW, then a universe that fails the FLRW tests but passes the isotropy tests violates the copernican principle.

### Re: [1104.1300] Is the Universe homogeneous?

Posted: **April 12 2011**

by **Syksy Rasanen**

Observing exact homogeneity and isotropy would prove that the universe is exactly FRW. But this is not the kind of a universe we live in.

Observing statistical homogeneity and isotropy on large scales does not prove that the universe is close to FRW. The FRW model describes an exactly homogeneous and isotropic universe, not one that is statistically homogeneous and isotropic.

### Re: [1104.1300] Is the Universe homogeneous?

Posted: **April 14 2011**

by **Boud Roukema**

Syksy Rasanen wrote:Observing exact homogeneity and isotropy would prove that the universe is exactly FRW. But this is not the kind of a universe we live in.

Since that may be too abstract for some people, here is a more concrete way of saying that. The Earth exists, with an overdensity of about [tex]10^{30}[/tex]. Virialised clusters of galaxies exist, with overdensities above 200. These are uncontroversial observational results. Hence, we do not live in an exactly F

LRW universe.

The FRW model describes an exactly homogeneous and isotropic universe, not one that is statistically homogeneous and isotropic.

In fact, the FLRW model describes an exactly

*locally* homogeneous and

*locally* isotropic universe. Some FLRW universes are locally homogeneous and locally isotropic, but globally inhomogeneous and/or globally anisotropic, e.g. an E_2 FLRW model better fits WMAP data than an R^3 FLRW model with the same (concordance model) metric:

1009.5880.