Testing General Relativity on Horizon Scales and the Primordial
  non-Gaussianity
  The proper general relativistic description of the observed galaxy power
spectrum is substantially different from the standard Newtonian description on
large scales, providing a unique opportunity to test general relativity on
horizon scales. Using the Einstein equations, the general relativistic effects
can be classified as two new terms that represent the velocity and the
gravitational potential, coupling to the time evolution of galaxy number
density and Hubble parameter. Compared to the dominant density and velocity
redshift-space distortion terms, the former scales as H/k and correlates the
real and imaginary parts of the Fourier modes, while the latter scales as
(H/k)^2, where k is the comoving wave number and H is the conformal Hubble
parameter. We use the recently developed methods to reduce the sampling
variance and shot noise to show that in an all sky galaxy redshift survey at
low redshift the velocity term can be measured at 10-sigma confidence level, if
one can utilize halos of mass M>10^{10} Msun, while the gravitational potential
term itself can only be marginally detected. We also demonstrate that the
general relativistic effect is not degenerate with the primordial non-Gaussian
signature in galaxy bias, and the ability to detect the primordial
non-Gaussianity is little compromised.
