Beyond the growth rate of cosmic structure: Testing modified gravity models with an extra degree of freedom

TL;DR

This paper explores how modifications to gravity, such as additional degrees of freedom, can be tested through cosmological structure formation measurements, using the Galileon model and WiggleZ survey data.

Contribution

It introduces the concept of stochastic bias in modified gravity models and demonstrates how redshift-space distortion data can constrain such theories.

Findings

Upper limit on conformal coupling strength |1/M| < 200 / Mp

Stochastic bias can affect interpretation of growth rate measurements

Constraints on fifth-force strength compared to gravity

Abstract

In 'modified' gravity the observed acceleration of the universe is explained by changing the gravitational force law or the number of degrees of freedom in the gravitational sector. Both possibilities can be tested by measurements of cosmological structure formation. In this paper we elaborate the details of such tests using the Galileon model as a case study. We pay attention to the possibility that each new degree of freedom may have stochastically independent initial conditions, generating different types of potential well in the early universe and breaking complete correlation between density and velocity power spectra. This 'stochastic bias' can confuse schemes to parametrize the predictions of modified gravity models, such as the use of the growth parameter f alone. Using data from the WiggleZ Dark Energy Survey we show that it will be possible to obtain constraints using information about the cosmological-scale force law embedded in the multipole power spectra of redshift-space distortions. As an example, we obtain an upper limit on the strength of the conformal coupling to matter in the cubic Galileon model, giving |1/M| < 200 / Mp. This allows the fifth-force to be stronger than gravity, but is consistent with zero coupling.