Secondorder cosmological perturbations. IV. Produced by scalartensor and tensortensor couplings during the radiation dominated stage
Abstract
We continue to study the secondorder cosmological perturbations in synchronous coordinates in the framework of general relativity (GR) during the radiation dominated (RD) stage and to focus on the scalartensor and tensortensor couplings. The firstorder curl velocity and the associated firstorder vector metric perturbations are assumed to be vanishing. By analytically solving the secondorder Einstein equation and the energymomentum conservation equations, we obtain the secondorder formal solutions (in the integral form) of all the metric perturbations, density contrast and velocity; perform the transformation between the synchronous coordinates; and identify the residual gauge modes in the secondorder solutions. In addition, we present the secondorder gauge transformations of the solutions from synchronous to Poisson coordinates. To apply these formal solutions to concrete cosmological study, one needs to choose proper initial conditions and carry out several numerical integrations.
 Publication:

Physical Review D
 Pub Date:
 June 2019
 DOI:
 10.1103/PhysRevD.99.123008
 arXiv:
 arXiv:1905.03272
 Bibcode:
 2019PhRvD..99l3008W
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 79 pages, 2 figures