Observed galaxy number counts on the lightcone up to second order: III. Magnification Bias

TL;DR

This paper calculates second-order galaxy number counts including magnification bias and all relativistic effects, crucial for precise cosmological measurements and understanding non-Gaussianity.

Contribution

It provides a comprehensive second-order relativistic framework for galaxy counts, incorporating all effects from observing on the light cone, including new terms.

Findings

Identifies new contributions to galaxy number counts.

Highlights importance of second-order effects for accurate cosmological inference.

Provides a detailed theoretical model for magnification bias in galaxy surveys.

Abstract

We study up to second order the galaxy number over-density that depends on magnification in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order which arise from observing on the past light cone, including all redshift and lensing distortions, contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. We find several new terms and contributions that could be potentially important for an accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates.