In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the right-handed mode and the left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard FðRÞ gravity.

We consider the self-potential and the self-force for an electrically charged particle at rest in the massive wormhole space-time. We develop general approach for the renormalization of electromagnetic field of such particle in the static space-times and apply it to the space-time of wormhole the metric of which is a solution to the Einstein-scalar field equations in the case of a phantom massless scalar field. The self-force is found in manifest form; it is an attractive force. We discuss the peculiarities due to the parameter of the wormhole mass.

We study the effect of one-loop vacuum polarization on photon propagation in Siklos spacetimes in the geometric optics limit. We show that for photons with a general polarization in the transverse plane, the quantum correction vanishes in spacetimes with Hxy = 0. For photons polarized along a transverse axis, subluminal and superluminal solutions are admitted for certain subclasses of Siklos spacetimes. We investigate the results in the Kaigorodov and Defrise spacetimes and obtain explicit expressions for the phase velocities. In Kaigorodov spacetime with H ∼ x 3 , photons polarized along x-axis are subluminal in regions where H is positive, and superluminal in regions where H is negative, while photons polarized along y-axis are superluminal in H > 0 regions and subluminal in H < 0 regions. In Defrise spacetime, H ∼ x −2 , x-polarized and y-polarized photons are superluminal for H < 0 and subluminal for H > 0. We comment on motion in other Siklos spacetimes.

We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.