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

Abstract

Assuming a ΛCDM universe in a single-field inflationary scenario,we compute the three-point correlation function of the observed matterdensity fluctuation in the squeezed triangular configuration, accountingfor all the relativistic effects at the second order in perturbations.This squeezed three-point correlation function characterizes the local-typeprimordial non-Gaussianity, and it has been extensively debated in literaturewhether there exists a prominent feature in galaxy clustering on large scalesin a single-field inflationary scenarioeither from the primordial origin or the intrinsic nonlinearity in generalrelativity. First, we show that theoretical descriptions of galaxy bias areincomplete in general relativity due to ambiguities in spatial gauge choice,while those of cosmological observables are independent of spatial gaugechoice. Hence a proper relativistic description of galaxy bias is neededto reach a definitive conclusion in galaxy clustering. Second, we demonstratethat the gauge-invariant calculations of the cosmologicalobservables remain unaffected by extra coordinate transformations like CFC orlarge diffeomorphism like dilatation. Finally, we show thatthe relativistic effects associated with light propagation inobservations cancel each other, and hence there exists nonon-Gaussian contribution from the so-called projection effectsin the squeezed three-point correlation function.