Hwang

Cosmological Post-Newtonian Approximation with Dark Energy
Jai-chan Hwang (Kyungpook National University)

We present general relativistic cosmological hydrodynamic equations with the post-Newtonian (PN) corrections. The PN approximation, based on the assumptions of weak gravitational fields and slow motions, provides a way to estimate general relativistic effects in the fully nonlinear evolution stage of the large-scale cosmic structures. We include the cosmological constant and a minimally coupled scalar field as the potential dark energy. We present the fully nonlinear cosmological 1PN equations in a form suitable for implementation in conventional Newtonian hydrodynamic simulations. Although the typical 1PN order terms are about 10^{-6} - 10^{-4} times smaller than the Newtonian terms, we cannot rule out possible presence of cumulative (secular) effects due to the time-delayed propagation of the relativistic gravitational field with finite speed. These relativistic correction terms could become important in future precision cosmology.