Relativistic effects and primordial non-Gaussianity in the matter density fluctuation

Understand

We present the third-order analytic solution of the matter density fluctuation in the proper-time hypersurface of nonrelativistic matter flows by solving the nonlinear general relativistic equations.

• The proper-time hypersurface provides a coordinate system that a local observer can set up without knowledge beyond its neighborhood, along with physical connections to the local Newtonian descriptions in the relativistic context.
• The initial condition of our analytic solution is set up by the curvature perturbation in the comoving gauge, clarifying its impact on the nonlinear evolution.
• We compute the effective non-Gaussian parameters due to the nonlinearity in the relativistic equations.