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

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.

26 pages. In the previous (and in the published paper), we mistakenly omitted some post-Born terms. This error has been corrected here. Typos in equations 64, 100 corrected

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