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Differentiating dark energy and modified gravity with galaxy redshift surveys

Yun Wang

TL;DR

The paper investigates distinguishing dark energy from modified gravity using galaxy redshift surveys by comparing the observed growth rate $f_g(z)$ with the gravity-free prediction $f_g^H(z)$ derived from the measured $H(z)$. ItForecasts a wide-area, deep magnitude-limited near-infrared (NIR) galaxy survey to achieve $H(z)$ measurements at the 1–2% level via BAO and $f_g(z)$ at the few-percent level via redshift-space distortions and galaxy bias across $0.5<z<2$, enabling a model-discriminating test of gravity. The analysis demonstrates that a survey covering about $11{,}931$ deg$^2$ could rule out DGP gravity at 99.99% CL when expansion histories are matched, providing a powerful, largely model-independent probe. The study argues feasibility with next-generation NASA/ESA space missions and highlights the potential for a transformative advance in understanding cosmic acceleration by decisively differentiating dark energy from modified gravity.

Abstract

The observed cosmic acceleration today could be due to an unknown energy component (dark energy), or a modification to general relativity (modified gravity). If dark energy models and modified gravity models are required to predict the same cosmic expansion history H(z), they will predict different growth rate for cosmic large scale structure, f_g(z)=d\ln δ/d\ln a (δ=(ρ_m-\bar{ρ_m})/\bar{ρ_m}), a is the cosmic scale factor). If gravity is not modified, the measured H(z) leads to a unique prediction for f_g(z), f_g^H(z). Comparing f_g^H(z) with the measured f_g(z) provides a transparent and straightforward test of gravity. We show that a simple χ^2 test provides a general figure-of-merit for our ability to distinguish between dark energy and modified gravity given the measured H(z) and f_g(z). We study a magnitude-limited NIR galaxy redshift survey covering >10,000 (deg)^2 and the redshift range of 0.5<z<2. The resultant data can be divided into 7 redshift bins, and yield the measurement of H(z) to the accuracy of 1-2% via baryon acoustic oscillation measurements, and f_g(z) to the accuracy of a few percent via the measurement of redshift space distortions and the bias factor which describes how light traces mass. We find that if the H(z) data are fit by both a DGP gravity model and an equivalent dark energy model that predict the same expansion history, a survey area of 11,931 (deg)^2 is required to rule out the DGP gravity model at the 99.99% confidence level. It is feasible for such a galaxy redshift survey to be carried out by the next generation space missions from NASA and ESA, and it will revolutionize our understanding of the universe by differentiating between dark energy and modified gravity.

Differentiating dark energy and modified gravity with galaxy redshift surveys

TL;DR

The paper investigates distinguishing dark energy from modified gravity using galaxy redshift surveys by comparing the observed growth rate with the gravity-free prediction derived from the measured . ItForecasts a wide-area, deep magnitude-limited near-infrared (NIR) galaxy survey to achieve measurements at the 1–2% level via BAO and at the few-percent level via redshift-space distortions and galaxy bias across , enabling a model-discriminating test of gravity. The analysis demonstrates that a survey covering about deg could rule out DGP gravity at 99.99% CL when expansion histories are matched, providing a powerful, largely model-independent probe. The study argues feasibility with next-generation NASA/ESA space missions and highlights the potential for a transformative advance in understanding cosmic acceleration by decisively differentiating dark energy from modified gravity.

Abstract

The observed cosmic acceleration today could be due to an unknown energy component (dark energy), or a modification to general relativity (modified gravity). If dark energy models and modified gravity models are required to predict the same cosmic expansion history H(z), they will predict different growth rate for cosmic large scale structure, f_g(z)=d\ln δ/d\ln a (δ=(ρ_m-\bar{ρ_m})/\bar{ρ_m}), a is the cosmic scale factor). If gravity is not modified, the measured H(z) leads to a unique prediction for f_g(z), f_g^H(z). Comparing f_g^H(z) with the measured f_g(z) provides a transparent and straightforward test of gravity. We show that a simple χ^2 test provides a general figure-of-merit for our ability to distinguish between dark energy and modified gravity given the measured H(z) and f_g(z). We study a magnitude-limited NIR galaxy redshift survey covering >10,000 (deg)^2 and the redshift range of 0.5<z<2. The resultant data can be divided into 7 redshift bins, and yield the measurement of H(z) to the accuracy of 1-2% via baryon acoustic oscillation measurements, and f_g(z) to the accuracy of a few percent via the measurement of redshift space distortions and the bias factor which describes how light traces mass. We find that if the H(z) data are fit by both a DGP gravity model and an equivalent dark energy model that predict the same expansion history, a survey area of 11,931 (deg)^2 is required to rule out the DGP gravity model at the 99.99% confidence level. It is feasible for such a galaxy redshift survey to be carried out by the next generation space missions from NASA and ESA, and it will revolutionize our understanding of the universe by differentiating between dark energy and modified gravity.

Paper Structure

This paper contains 2 sections, 11 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Models

Figures (1)

  • Figure 1: Current and expected future measurements of the cosmic expansion history $H(z)=H_0 E(z)$ and the growth rate of cosmic large scale structure $f_g(z)=d\ln \delta/d\ln a$ ($\delta=(\rho_m-\overline{\rho_m})/ \overline{\rho_m})$, $a$ is the cosmic scale factor). Note that the fiducial model assumed for the future galaxy redshift survey is a dark energy model with the same $H(z)$ as that of the DGP model. These two models have identical expansion histories $H(z)$ [solid line in panel (a)], but very different growth rates $f_g(z)$ [solid and dashed lines in panel (b)].