# Constraining DHOST theories with linear growth of matter density fluctuations

## TL;DR

This paper develops a formalism to analyze how cosmological observations, especially galaxy surveys, can constrain DHOST theories by examining the linear growth of matter density fluctuations, providing new bounds on these theories.

## Contribution

It introduces a new formalism for the evolution of matter fluctuations in DHOST theories and derives constraints from current observational data, breaking degeneracies without pulsar constraints.

## Key findings

- New constraints on DHOST parameter space
- Formalism for matter fluctuation evolution in DHOST
- Degeneracy breaking without pulsar data

## Abstract

We investigate the potential of cosmological observations, such as galaxy surveys, for constraining degenerate higher-order scalar-tensor (DHOST) theories, focusing in particular on the linear growth of the matter density fluctuations. We develop a formalism to describe the evolution of the matter density fluctuations during the matter dominated era and in the early stage of the dark energy dominated era in DHOST theories, and give an approximate expression for the gravitational growth index in terms of several parameters characterizing the theory and the background solution under consideration. By employing the current observational constraints on the growth index, we obtain a new constraint on a parameter space of DHOST theories. Combining our result with other constraints obtained from the Newtonian stellar structure, we show that the degeneracy between the effective parameters of DHOST theories can be broken without using the Hulse-Taylor pulsar constraint.