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arXiv · 2106.15139

Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole

Yonadav Barry Ginat·Vincent Desjacques·Donghui Jeong·Fabian Schmidt
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Abstract

We present a fully non-linear and relativistically covariant expression for the observed galaxy density contrast. Building on a null tetrad tailored to the cosmological observer's past light cone, we find a decomposition of the non-linear galaxy over-density into manifestly gauge-invariant quantities, each of which has a clear physical interpretation as a cosmological observable. This ensures that the monopole of the galaxy over-density field (the mean galaxy density as a function of observed redshift) is properly accounted for. We anticipate that this decomposition will be useful for future work on non-linearities in galaxy number counts, for example, deriving the relativistic expression for the galaxy bispectrum. We then specialise our results to conformal Newtonian gauge, with a Hubble parameter either defined globally or measured locally, illustrating the significance of the different contributions to the observed monopole of the galaxy density.

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Yonadav Barry Ginat, Vincent Desjacques, Donghui Jeong, Fabian Schmidt. 2021-06-29. Covariant Decomposition of The Non-Linear Galaxy Number Counts and Their Monopole. https://doi.org/10.1088/1475-7516%2F2021%2F12%2F031

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