Challenges in Connecting Modified Gravity Theory and Observations

TL;DR

Connecting modified gravity theories to observations is complex due to multiple free functions, and simple parametrizations often misestimate or miss signatures of modifications, especially in broad classes like Horndeski gravity.

Contribution

The paper demonstrates that simple parametrizations of property functions in modified gravity theories are ineffective and can lead to incorrect conclusions about observable signatures.

Findings

Simple parametrizations like $\alpha_i(t)\propto\Omega_{ m de}(t)$ are inaccurate.

Oversimplified property functions can miss signatures of modified gravity.

Tensor perturbations play a role in testing gravity modifications.

Abstract

Cosmic acceleration may be due to modifications of cosmic gravity and to test this we need robust connections between theory and observations. However, in a model independent approach like effective field theory or a broad class like Horndeski gravity, several free functions of time enter the theory. We show that simple parametrizations of these functions are unlikely to be successful; in particular the approximation $\alpha_i(t)\propto\Omega_{\rm de}(t)$ drastically misestimates the observables. This holds even in simple modified gravity theories like $f(R)$. Indeed, oversimplified approximations to the property functions $\alpha_i(t)$ can even miss the signature of modified gravity. We also consider the question of consistency relations and the role of tensor (gravitational wave) perturbations.