Galaxy Two-Point Correlation Function in General Relativity

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We perform theoretical and numerical studies of the full relativistic two-point galaxy correlation function, considering the linear-order scalar and tensor perturbation contributions and the wide-angle effects.

• Using the gauge-invariant relativistic description of galaxy clustering and accounting for the contributions at the observer position, we demonstrate that the complete theoretical expression is devoid of any long-mode contributions from scalar or tensor perturbations and it lacks the infrared divergences in agreement with the equivalence principle.
• By showing that the gravitational potential contribution to the correlation function converges in the infrared, our study justifies an IR cut-off $(k_{\text{IR}} \leq H_0)$ in computing the gravitational potential contribution.
• Using the full gauge-invariant expression, we numerically compute the galaxy two-point correlation function and study the individual contributions in the conformal Newtonian gauge.