Nonlinear perturbations in Relativistic cosmology

Abstract

In this dissertation, we discuss the inhomogeneity growth in the universe. The inhomogeneity growth is originated from the gravitational instability and we consider the Newtonian and the Einstein gravity in this dissertation. In the Newtonian cosmology based on the Newtonian gravity, we derive the nonlinear order solutions with the nonlinear perturbation theory, and show the next-leading-order power spectrum. The next-leading-order Newtonain power spectrum is effective on the small scale. However, the Newtonian cosmology is only appropriate to study subhorion scale. To overcome the limitation of the Newtonian cosmology, we need to study the Relativistic cosmology based on the Einstein gravity. In the Relativistic, we discuss the gauge issue and show that the proper time gauge is relevant to study the universe. We also derive the higher solutions in the proper time gauge and show the next-leading-order power spectra. From the synchronous gauge nonlinear order study, we conclude that the synchronous gauge is improper and the comoving gauge is proper to study nonlinear perturbation. Furthermore, we show the next-leading-order bispectrum in the comoving guage and the relativistic effect is much smaller than the Newtonian results. At the end or this dissertation, we study the Dark energy effect on the (nonlinear)inhomogeneity growth, and the Dark energy affects significantly the Relativistic next-leading-order power spectrum rather than the Newtonian power spectrum.