Cosmological Parameter Estimation with Large Scale Structure Observations

TL;DR

This paper evaluates the potential of future galaxy surveys to improve cosmological parameter estimates by using relativistically corrected angular power spectra, comparing new methods with traditional $P(k)$ analysis.

Contribution

It introduces a relativistic $C_ll(z_1,z_2)$ method for cosmological analysis and compares its effectiveness against standard $P(k)$ methods for different survey types.

Findings

The new $C_ll(z_1,z_2)$ method outperforms $P(k)$ analysis for photometric surveys.

Spectroscopic surveys face shot noise limitations despite the potential of the new method.

Certain surveys can effectively measure lensing contributions and analyze the monopole component.

Abstract

We estimate the sensitivity of future galaxy surveys to cosmological parameters, using the redshift dependent angular power spectra of galaxy number counts, $C_\ell(z_1,z_2)$, calculated with all relativistic corrections at first order in perturbation theory. We pay special attention to the redshift dependence of the non-linearity scale and present Fisher matrix forecasts for Euclid-like and DES-like galaxy surveys. We compare the standard $P(k)$ analysis with the new $C_\ell(z_1,z_2)$ method. We show that for surveys with photometric redshifts the new analysis performs significantly better than the $P(k)$ analysis. For spectroscopic redshifts, however, the large number of redshift bins which would be needed to fully profit from the redshift information, is severely limited by shot noise. We also identify surveys which can measure the lensing contribution and we study the monopole, $C_0(z_1,z_2)$.