Abstract
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. With proper coordinate rescaling, we show that the equivalence principle is respected and the relativistic effect vanishes in the large-scale limit.
| Original language | English |
|---|---|
| Pages (from-to) | 94-98 |
| Number of pages | 5 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 754 |
| DOIs | |
| State | Published - 10 Mar 2016 |
Bibliographical note
Funding Information:We acknowledge useful discussions with Mehrdad Mirbabayi and David Wands. We are especially grateful to Matias Zaldarriaga for the critical comments on the manuscript and Jai-chan Hwang for sharing his unpublished results, to which we compare our results. J.Y. is supported by the Swiss National Science Foundation . J.G. is supported by the Independent Junior Research Fellowship and by a Starting Grant through the Basic Science Research Program of the National Research Foundation of Korea ( 2013R1A1A1006701 ).
Publisher Copyright:
© 2016 The Authors.