Does the Isotropy of the CMB Imply a Homogeneous Universe? Some Generalised EGS Theorems

TL;DR

This paper extends EGS theorems by showing that high CMB isotropy and the Copernican principle alone do not guarantee a homogeneous universe unless the observers are non-accelerating, highlighting the importance of acceleration in cosmological models.

Contribution

It introduces generalized EGS theorems that incorporate observer acceleration, providing conditions under which isotropy implies homogeneity in more complex cosmological models.

Findings

Accelerating observers can lead to inhomogeneous spacetimes despite isotropic CMB.

Non-accelerating (geodesic) observers in these models imply the universe is FLRW.

Theorems are extended to multi-component fluids with scalar fields or cosmological constant.

Abstract

We demonstrate that the high isotropy of the Cosmic Microwave Background (CMB), combined with the Copernican principle, is not sufficient to prove homogeneity of the universe -- in contrast to previous results on this subject. The crucial additional factor not included in earlier work is the acceleration of the fundamental observers. We find the complete class of irrotational perfect fluid spacetimes admitting an exactly isotropic radiation field for every fundamental observer and show that are FLRW if and only if the acceleration is zero. While inhomogeneous in general, these spacetimes all possess three-dimensional symmetry groups, from which it follows that they also admit a thermodynamic interpretation. In addition to perfect fluids models we also consider multi-component fluids containing non-interacting radiation, dust and a quintessential scalar field or cosmological constant in which the radiation is isotropic for the geodesic (dust) observers. It is shown that the non-acceleration of the fundamental observers forces these spacetimes to be FLRW. While it is plausible that fundamental observers (galaxies) in the real universe follow geodesics, it is strictly necessary to determine this from local observations for the cosmological principle to be more than an assumption. We discuss how observations may be used to test this.