# Matter Power Spectra in Viable $f(R)$ Gravity Models with Dynamical Background

## TL;DR

This paper investigates how viable $f(R)$ gravity models with dynamic backgrounds influence the matter power spectrum, showing they tend to shorten the universe's age and suppress density fluctuations, with implications for neutrino mass constraints.

## Contribution

It introduces a detailed analysis of matter power spectra in $f(R)$ models considering dynamical backgrounds, using observational data to constrain model parameters.

## Key findings

- Viable $f(R)$ models shorten the universe's age.
- They suppress matter density fluctuations.
- Dynamical dark energy evolution constrains neutrino masses.

## Abstract

We study the matter power spectra in the viable $f(R)$ gravity models with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We show that these viable $f(R)$ models generally shorten the age of the universe and suppress the matter density fluctuation. We examine the allowed ranges of the model parameters and the constraints of the cosmological variables from the current observational data, and find that the dynamical evolution of $\rho_{DE}(z)$ plays an important role to constrain the neutrino masses.