Consistency test of general relativity from large scale structure of the Universe

TL;DR

This paper proposes a novel consistency test of General Relativity on cosmological scales by comparing reconstructed and observed lensing spectra, aiming to distinguish between dark energy and modified gravity explanations for cosmic acceleration.

Contribution

It introduces a new observational consistency relation in GR and a method to test it using weak lensing, density perturbations, and peculiar velocities.

Findings

The consistency relation can be tested with current and future cosmological data.

Any inconsistency indicates a deviation from GR, suggesting modified gravity.

The method provides a way to differentiate between dark energy and modified gravity models.

Abstract

We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models based on GR and modified gravity models without dark energy. We derive the consistency relation in GR which is written only in terms of observables - the Hubble parameter, the density perturbations, the peculiar velocities and the lensing potential. The breakdown of this consistency relation implies that the Newton constant which governs large-scale structure is different from that in the background cosmology, which is a typical feature in modified gravity models. We propose a method to perform this test by reconstructing the weak lensing spectrum from measured density perturbations and peculiar velocities. This reconstruction relies on Poisson's equation in GR to convert the density perturbations to the lensing potential. Hence any inconsistency between the reconstructed lensing spectrum and the measured lensing spectrum indicates the failure of GR on cosmological scales. The difficulties in performing this test using actual observations are discussed.