# Investigating the degeneracy between modified gravity and massive neutrinos with redshift-space distortions

## TL;DR

This paper explores how redshift-space distortions can help distinguish between modified gravity and massive neutrinos, by modeling non-linear effects to break their degeneracy in the matter power spectrum.

## Contribution

It introduces an extended perturbation theory model for non-linear RSD that accounts for both Hu-Sawicki f(R) gravity and massive neutrinos to improve discrimination.

## Key findings

- Degeneracy can be broken if the linear growth rate is accurately recovered from RSD.
- Non-linear modeling is essential for distinguishing modified gravity from neutrino effects.
- The extended model improves the interpretation of RSD signals in cosmological tests.

## Abstract

There is a well known degeneracy between the enhancement of the growth of large-scale structure produced by modified gravity models and the suppression due to the free-streaming of massive neutrinos at late times. This makes the matter power-spectrum alone a poor probe to distinguish between modified gravity and the concordance $\Lambda$CDM model when neutrino masses are not strongly constrained. In this work, we investigate the potential of using redshift-space distortions (RSD) to break this degeneracy when the modification to gravity is scale-dependent in the form of Hu-Sawicki $f(R)$. We find that if the linear growth rate can be recovered from the RSD signal, the degeneracy can be broken at the level of the dark matter field. However, this requires accurate modelling of the non-linearities in the RSD signal, and we here present an extension of the standard perturbation theory-based model for non-linear RSD that includes both Hu-Sawicki $f(R)$ modified gravity and massive neutrinos.