Non-Gaussianity in the squeezed three-point correlation from the relativistic effects

Assuming a ΛCDM universe in a single-field inflationary scenario, we compute the three-point correlation function of the observed matter density fluctuation in the squeezed triangular configuration, accounting for all the relativistic effects at the second order in perturbations. This squeezed three-point correlation function characterizes the local-type primordial non-Gaussianity, and it has been extensively debated in literature whether there exists a prominent feature in galaxy clustering on large scales in a single-field inflationary scenario either from the primordial origin or the intrinsic nonlinearity in general relativity. First, we show that theoretical descriptions of galaxy bias are incomplete in general relativity due to ambiguities in spatial gauge choice, while those of cosmological observables are independent of spatial gauge choice. Hence a proper relativistic description of galaxy bias is needed to reach a definitive conclusion in galaxy clustering. Second, we demonstrate that the gauge-invariant calculations of the cosmological observables remain unaffected by extra coordinate transformations like CFC or large diffeomorphism like dilatation. Finally, we show that the relativistic effects associated with light propagation in observations cancel each other, and hence there exists no non-Gaussian contribution from the so-called projection effects in the squeezed three-point correlation function