On Exact Anisotropic Solutions of Kasner type in Higher Order Gravities

Abstract

This thesis has considered the existence of anisotropic exact vacuum solutions in the context of higher order gravities. The investigated models generally are a function of three scalars R, $R_{\alpha\beta}R^{\alpha\beta}$ and $R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu}$. Near singularity, dominant terms in the expansion of analytic type of these functions are in terms of $R^{n}$ (practically $R^{1+\delta}$, for indicating deviation from Einstein-Hilbert action), ($R_{\alpha\beta}R^{\alpha\beta})^{n}$ or ($R_{\alpha\beta\mu\nu}R^{\alpha\beta\mu\nu})^{n}$. Investigation shows that there always exists Kasner type solutions in $R^{n}$ and $R_{\alpha\beta}R^{\alpha\beta})^{n}$ models. But, in the third type model, anisotropic Kasner type solution has not been found. Furthermore, the behavior of these models in the presence of matter has been investigated, and it has been revealed that these solutions are always valid for relativistic matter, however this is not true for some non relativistic matter. Moreover, the energy condition for $R^{1+\delta}$ model in vacuum has been investigated and has been shown that the application of four energy conditions (weak, null, strong and dominant) leads to one constraint on $\delta$.