We present a novel approach to compute systematically the relativistic projection effects at any order in perturbation theory within the weak field approximation. In this derivation the galaxy number counts is written completely in terms of the redshift perturbation. The relativistic effects break the symmetry along the line-of-sight and they source, contrarily to the standard perturbation theory, the odd multipoles of the matter power spectrum or 2-point correlation function, providing a unique signature for their detection in Large Scale Structure surveys. We show that our approach agrees with previous derivations (up to third order) of relativistic effects and, for the first time, we derive a model for the transverse Doppler effect. Moreover, we proof that in the Newtonian limit this approach is consistent with standard perturbation theory at any order.
|Number of pages||16|
|Journal||Journal of Cosmology and Astroparticle Physics (JCAP)|
|Publication status||Published - 29 Sep 2020|