In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales - even if the primordial metric perturbation is
Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.
We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects -- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the g
ravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f_NL is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.
