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Single-Field Consistency Relations of Large Scale Structure. Part III: Test of the Equivalence Principle

Paolo Creminelli, Jérôme Gleyzes, Lam Hui, Marko Simonović, Filippo Vernizzi

TL;DR

This work extends single-field consistency relations for Large Scale Structure to test the Equivalence Principle (EP) on cosmological scales. By analyzing a two-fluid toy model with a fifth-force coupling, the authors show that EP violation introduces a dipolar $1/q$ term in the squeezed limit of the equal-time bispectrum, with amplitude proportional to $\alpha^2$ and the B-fluid fraction $w_B$. They develop a forecast framework for detecting this signal using the galaxy bispectrum, and provide concrete estimates suggesting cosmological surveys could constrain EP violations beyond current Solar System bounds in some scenarios, while Galileon models do not produce such violations. The results indicate that a robust, model-agnostic test of EP on large scales is feasible with upcoming data, offering a complementary probe to existing gravity tests and guiding explorations of modified gravity theories.

Abstract

The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looking at the squeezed limit of the 3-point function involving two populations of objects. We find that one can explore EP violations of order 10^{-3} - 10^{-4} on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a very tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models.

Single-Field Consistency Relations of Large Scale Structure. Part III: Test of the Equivalence Principle

TL;DR

This work extends single-field consistency relations for Large Scale Structure to test the Equivalence Principle (EP) on cosmological scales. By analyzing a two-fluid toy model with a fifth-force coupling, the authors show that EP violation introduces a dipolar term in the squeezed limit of the equal-time bispectrum, with amplitude proportional to and the B-fluid fraction . They develop a forecast framework for detecting this signal using the galaxy bispectrum, and provide concrete estimates suggesting cosmological surveys could constrain EP violations beyond current Solar System bounds in some scenarios, while Galileon models do not produce such violations. The results indicate that a robust, model-agnostic test of EP on large scales is feasible with upcoming data, offering a complementary probe to existing gravity tests and guiding explorations of modified gravity theories.

Abstract

The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looking at the squeezed limit of the 3-point function involving two populations of objects. We find that one can explore EP violations of order 10^{-3} - 10^{-4} on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a very tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models.

Paper Structure

This paper contains 7 sections, 35 equations, 1 figure.

Table of Contents

  1. Introduction
  2. An example of equivalence principle violation
  3. Detecting an equivalence principle violation
  4. Signal to noise for the bispectrum
  5. Estimate for our toy model
  6. Modifications of gravity and equivalence principle violation
  7. Conclusions

Figures (1)

  • Figure 1: Expected error on $\alpha^2$, $\sigma (\alpha^2)$, for a survey with volume $V=1(\mathrm{Gpc}/h)^3$ at three different redshifts, $z=0$, $z=0.5$ and $z=1$. Left: $\sigma (\alpha^2)$ is plotted as a function of $k_{\mathrm{max}}$. We have chosen $k_{\rm min} = 2 \pi/V^{1/3}$ so that the violation of the EP extends to the whole survey. Right: $\sigma (\alpha^2)$ is plotted as a function of $k_{\mathrm{min}}$. $k_{\rm max}$ is given by $0.10, \, 0.14, \, 0.19$ for $z=0, \, 0.5, \, 1$ respectively. The dotted lines represent $\alpha^2 \lesssim 10^{-6} (m/H)^2$, i.e. the bound on $\alpha^2$ from screening the Milky Way Wang:2012kj.