# Parametrizing modified gravity for cosmological surveys

## TL;DR

This paper investigates how simple parametrizations with few parameters can effectively describe complex modified gravity theories in cosmological surveys, emphasizing the importance of stability and smoothness in the models.

## Contribution

It demonstrates that simple, smooth parametrizations with two parameters per function are generally sufficient to fit complex theories, reducing the theory space for practical cosmological analysis.

## Key findings

- Simple parametrizations are often adequate for complex theories.
- Stability constraints significantly limit the theory space.
- Two-parameter models are preferred in most cases according to BIC.

## Abstract

One of the challenges in testing gravity with cosmology is the vast freedom opened when extending General Relativity. For linear perturbations, one solution consists in using the Effective Field Theory of Dark Energy (EFT of DE). Even then, the theory space is described in terms of a handful of free functions of time. This needs to be reduced to a finite number of parameters to be practical for cosmological surveys. We explore in this article how well simple parametrizations, with a small number of parameters, can fit observables computed from complex theories. Imposing the stability of linear perturbations appreciably reduces the theory space we explore. We find that observables are not extremely sensitive to short time-scale variations and that simple, smooth parametrizations are usually sufficient to describe this theory space. Using the Bayesian Information Criterion, we find that using two parameters for each function (an amplitude and a power law index) is preferred over complex models for 86% of our theory space.