Curvature constraints from Large Scale Structure

TL;DR

This paper enhances the CLASS code to include relativistic effects in galaxy counts within curved geometries, analyzing their impact on measuring spatial curvature with future surveys, and highlighting potential biases if effects like cosmic magnification are neglected.

Contribution

It introduces a modified version of the CLASS code incorporating relativistic corrections for curved geometries and assesses their impact on curvature measurements.

Findings

Relativistic effects significantly bias curvature estimates if neglected.

Cosmic magnification is the most impactful relativistic correction.

Other effects are subdominant in the studied configurations.

Abstract

We modified the CLASS code in order to include relativistic galaxy number counts in spatially curved geometries; we present the formalism and study the effect of relativistic corrections on spatial curvature. The new version of the code is now publicly available. Using a Fisher matrix analysis, we investigate how measurements of the spatial curvature parameter $\Omega_K$ with future galaxy surveys are affected by relativistic effects, which influence observations of the large scale galaxy distribution. These effects include contributions from cosmic magnification, Doppler terms and terms involving the gravitational potential. As an application, we consider angle and redshift dependent power spectra, which are especially well suited for model independent cosmological constraints. We compute our results for a representative deep, wide and spectroscopic survey, and our results show the impact of relativistic corrections on the spatial curvature parameter estimation. We show that constraints on the curvature parameter may be strongly biased if, in particular, cosmic magnification is not included in the analysis. Other relativistic effects turn out to be subdominant in the studied configuration. We analyze how the shift in the estimated best-fit value for the curvature and other cosmological parameters depends on the magnification bias parameter, and find that significant biases are to be expected if this term is not properly considered in the analysis.