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

Yong-Seon Song, Kazuya Koyama

TL;DR

This work addresses the question of whether General Relativity remains valid on cosmological scales or if modified gravity is needed to explain late-time acceleration. It develops an observable GR consistency framework that connects the expansion history $H$, density perturbations $\delta_t$, peculiar velocities, and the lensing potential $\Phi_-$, and then constructs a practical test by reconstructing the weak-lensing spectrum from density and velocity measurements using the GR Poisson equation. The authors introduce estimators $\mathcal{R}_{\ell}(\alpha^{(1)})$ and $\mathcal{R}_{\ell}(\alpha^{(2)})$ based on projected power spectra to compare reconstructed and observed lensing signals, validating the approach with MG models such as $f(R)$ and DGP where deviations exceed reconstruction errors. They also discuss key systematic uncertainties (bias, redshift distributions, redshift-space distortions) and outline how upcoming surveys could realistically implement this model-independent test to distinguish MG from clustering dark energy, thereby providing a robust falsification mechanism for GR on cosmic scales.

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.

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

TL;DR

This work addresses the question of whether General Relativity remains valid on cosmological scales or if modified gravity is needed to explain late-time acceleration. It develops an observable GR consistency framework that connects the expansion history , density perturbations , peculiar velocities, and the lensing potential , and then constructs a practical test by reconstructing the weak-lensing spectrum from density and velocity measurements using the GR Poisson equation. The authors introduce estimators and based on projected power spectra to compare reconstructed and observed lensing signals, validating the approach with MG models such as and DGP where deviations exceed reconstruction errors. They also discuss key systematic uncertainties (bias, redshift distributions, redshift-space distortions) and outline how upcoming surveys could realistically implement this model-independent test to distinguish MG from clustering dark energy, thereby providing a robust falsification mechanism for GR on cosmic scales.

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.

Paper Structure

This paper contains 6 sections, 37 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Background and perturbations
  3. Consistency test of GR
  4. Consistency test from projected power spectrum
  5. Systematic errors in consistency test
  6. Conclusion

Figures (1)

  • Figure 1: Upper panel: The precision test between $C_{\ell}^{s\,dd}$ (solid curves) and $\tilde{C}_{\ell}^{s\,dd}$ with a redshift spacing $\Delta z_i = 0.1$ (dash curves) for 6 different $z_s$ running from 0.25 (bottom) to 2.75 (top). We restricted the reconstructed power spectra to scales where the non-liner effects give less than $5\%$ changes on the power spectra. Middle panel: The first consistency test for GR model (solid curves) and MG model -f(R) gravity Song:2006ej (long dash curves). Bottom panel: The second consistency test for GR model (solid curves), sDGP model lue04koyama05 (dash curves), and nDGP model Song:2007wdCardoso:2007xc(dotted curves).