# Cosmological information content in redshift-space power spectrum of SDSS-like galaxies in the quasi-nonlinear regime up to $k=0.3\,h\,$Mpc$^{-1}$

## TL;DR

This study demonstrates that combining monopole and quadrupole galaxy power spectra up to $k=0.3 h$ Mpc$^{-1}$ significantly enhances the precision of cosmological parameter estimates from SDSS-like galaxy surveys, even after accounting for galaxy-halo connection uncertainties.

## Contribution

It introduces a comprehensive Fisher matrix analysis using high-resolution simulations to quantify the cosmological information in redshift-space power spectra up to $k=0.3 h$ Mpc$^{-1}$, including nuisance parameters.

## Key findings

- Combining monopole and quadrupole spectra improves parameter constraints.
- Including data up to $k=0.3 h$ Mpc$^{-1}$ increases information content by a factor of 6.
- Accurate cosmological and distance measurements are achievable despite galaxy-halo connection uncertainties.

## Abstract

Clustering properties and peculiar velocities of halos in large-scale structure carry a wealth of cosmological information over a wide range of scales from linear to nonlinear scales. We use halo catalogs in a suite of high-resolution $N$-body simulations to construct mock catalogs of galaxies that resemble the SDSS-like luminous early-type galaxies at three redshift bins in the range $0.15\le z\le 0.7$. To do this we include 10 nuisance parameters to model variations in halo-galaxy connections for each redshift bin; the halo occupation distribution, and the spatial and velocity distributions of galaxies in the host halos. We evaluate the Fisher information matrix for the redshift-space power spectrum of SDSS-like galaxies using different sets of the mock catalogs that are generated from changes in each of model parameters; cosmological parameters ($\sigma_8$ and $\Omega_{\rm m}$), the halo-galaxy connection parameters, and the cosmological distances ($D_{\rm A}$ and $H$ parameters at each redshift bin) for modeling an apparent geometrical distortion of the redshift-space power spectrum (the Alcock-Paczynski effect). We show that combining the monopole and quadrupole power spectra of galaxies allows for accurate estimations of the cosmological parameters and the cosmological distances, even after marginalization over the halo-galaxy parameters, by lifting the parameter degeneracies that are otherwise inevitable if either of the two spectra alone is used. When including the galaxy power spectrum information up to $k=0.3\,h\,$Mpc$^{-1}$, we find about factor of 6 gain in the cosmological information content of ($\sigma_8,\Omega_{\rm m},D_{\rm A}$'s and $H$'s) compared to $k=0.2\,h\,$Mpc$^{-1}$.