The impact of the Universe's expansion rate on constraints on modified growth of structure

TL;DR

This paper investigates how assumptions about the Universe's expansion rate influence constraints on modified gravity, finding current data limits the impact of these assumptions on the constraints of structure growth modifications.

Contribution

It demonstrates that current constraints on modifications to gravity are largely insensitive to the background expansion assumptions, using Gaussian Processes for model-independent analysis.

Findings

Constraints on Poisson modifications range between 10-20%.

Assumptions about expansion rate have minimal impact on current constraints.

Degeneracy exists between Poisson modifications and matter density, $\

Abstract

In the context of modified gravity, at linear level, the growth of structure in the Universe will be affected by modifications to the Poisson equation and by the background expansion rate of the Universe. It has been shown that these two effects lead to a degeneracy which must be properly accounted for if one is to place reliable constraints on new forces on large scales or, equivalently, modifications to General Relativity. In this paper we show that current constraints are such that assumptions about the background expansion have little impact on constraints on modifications to gravity. We do so by considering the background of a $\Lambda$ Cold Dark Matter ($\Lambda$CDM) universe, a universe with a more general equation of state for the dark energy, and finally, a general, model-independent, expansion rate. We use Gaussian Processes to model modifications to Poisson's equation and, in the case of a general expansion rate, to model the redshift dependent Hubble rate. We identify a degeneracy between modifications to Poisson's equation and the background matter density, $\Omega_M$, which can only be broken by assuming a model-dependent expansion rate. We show that, with current data, the constraints on modifications to the Poisson equation via measurements of the growth rate range between $10-20\%$ depending on the strength of our assumptions on the Universe's expansion rate.