Time drift of cosmological redshifts as a test of the Copernican principle

TL;DR

This paper proposes using the time drift of cosmological redshifts as a novel observational test to verify the Copernican principle and to reconstruct the universe's geometry, especially in inhomogeneous models.

Contribution

It introduces a method to test the Copernican principle via redshift drift measurements and reconstructs spacetime geometry from background observations in spherically symmetric models.

Findings

Time drift of redshift can test universe homogeneity.

Combining redshift drift with distance data reconstructs spacetime geometry.

Method distinguishes between homogeneous and inhomogeneous cosmological models.

Abstract

We present the time drift of the cosmological redshift in a general spherically symmetric spacetime. We demonstrate that its observation would allow us to test the Copernican principle and so determine if our universe is radially inhomogeneous, an important issue in our understanding of dark energy. In particular, when combined with distance data, this extra observable allows one to fully reconstruct the geometry of a spacetime describing a spherically symmetric under-dense region around us, purely from background observations.