Complementary consistency test of the Copernican principle via Noether's theorem and machine learning forecasts

TL;DR

This paper introduces a novel test of the Copernican principle using Noether's theorem and machine learning, which can effectively distinguish between standard cosmology and alternative models like void scenarios.

Contribution

It presents a new theoretical null test of the Copernican principle based on Noether's theorem and demonstrates its effectiveness with simulated data from future galaxy surveys.

Findings

The test can rule out certain void models at >3σ confidence.

Simulations show the test constrains deviations from the cosmological constant.

Forecasts indicate strong potential for upcoming surveys to validate the Copernican principle.

Abstract

The Copernican principle (CP), i.e. the assumption that we are not privileged observers of the Universe, is a fundamental tenet of the standard cosmological model. A violation of this postulate implies the possibility that the apparent cosmic acceleration could be explained without the need of a cosmological constant, dark energy or paper we present a new test of the CP relating the distance and the expansion rate, derived via Noether's theorem, which is complementary to other tests found in the literature. We also simulate fiducial data based on upcoming stage IV galaxy surveys and use them to reconstruct the Hubble rate $H(z)$ and the angular diameter distance $d_A(z)$ in order to forecast how well our null test can constrain deviations from the cosmological constant model. We find that our new test can easily rule out several scenarios based on the Lema\^{\i}tre-Tolman-Bondi void model at confidence of $\gtrsim 3\sigma$ at middle to high redshifts ($z>0.5$).