Numerical Relativity Investigation of the Effects of Gravitational Waves on the Inhomogeneity of the Universe

We numerically integrate the Einstein’s equations for a spatially flat Friedmann-Lemaire-Robertson-Walker (FLRW) background spacetime with a spatial curvature perturbation and evolving primordial tensor perturbations using the Einstein Toolkit. We find that although the primordial tensor perturbation doesn’t play an important role in the evolution of the overdensity produced by the scalar perturbation, there is an obvious imprint left by the primordial tensor perturbation on the distribution of the fractional density perturbation in the nonlinear region. This imprint may be a possible probe of a gravitational waves background in the future.