Non-Gaussianity in the Squeezed Three-Point Correlation from the
  Relativistic Effects
  Assuming a LCDM 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.
