Is the Universe homogeneous?

TL;DR

This paper explores the observational and theoretical challenges in establishing the universe's homogeneity, emphasizing the role of the Copernican Principle and the limitations of current data in proving large-scale uniformity.

Contribution

It clarifies the connection between isotropy and homogeneity, discusses the implications of CMB observations, and highlights the open questions in testing cosmic homogeneity.

Findings

Vanishing low multipoles of the CMB imply homogeneity.

Current observations suggest near-isotropy but do not prove homogeneity.

Proving large-scale homogeneity remains an open challenge.

Abstract

The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we interpret observations of the CMB and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past lightcone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity, we need to assume the Copernican Principle. First, we discuss the link between isotropic observations on the past lightcone and isotropic spacetime geometry: what observations do we need to be isotropic in order to deduce spacetime isotropy? Second, we discuss what we can say with the Copernican assumption. The most powerful result is based on the CMB: the vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to impose homogeneity. Real observations lead to near-isotropy on large scales - does this lead to near-homogeneity? There are important partial results, and we discuss why this remains a difficult open question. Thus we are currently unable to prove homogeneity of the Universe on large-scales, even with the Copernican Principle. However we can use observations of the CMB, galaxies and clusters to test homogeneity itself.