Effects of Nonlinear Inhomogeneity on the Cosmic Expansion with Numerical Relativity

We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure the departure of the average expansion rate with respect to this homogeneous and isotropic reference model, comparing local quantities to the predictions of linear perturbation theory. We find that collapsing perturbations reach the turnaround point much earlier than expected from the reference spherical top-hat collapse model and that the local deviation of the expansion rate from the homogeneous one can be as high as 28% at an underdensity, for an initial density contrast of 10^{-2}. We then study, for the first time, the exact behavior of the backreaction term Q_{D}. We find that, for small values of the initial perturbations, this term exhibits a 1/a scaling, and that it is negative with a linearly growing absolute value for larger perturbation amplitudes, thereby contributing to an overall deceleration of the expansion. Its magnitude, on the other hand, remains very small even for relatively large perturbations.

Does small scale structure significantly affect cosmological dynamics?

The large-scale homogeneity and isotropy of the Universe is generally thought to imply a well-defined background cosmological model. It may not. Smoothing over structure adds in an extra contribution, transferring power from small scales up to large. Second-order perturbation theory implies that the effect is small, but suggests that formally the perturbation series may not converge. The amplitude of the effect is actually determined by the ratio of the Hubble scales at matter-radiation equality and today-which are entirely unrelated. This implies that a universe with significantly lower temperature today could have significant backreaction from more power on small scales, and so provides the ideal testing ground for understanding backreaction. We investigate this using two different N-body numerical simulations-a 3D Newtonian and a 1D simulation which includes all relevant relativistic effects. We show that while perturbation theory predicts an increasing backreaction as more initial small-scale power is added, in fact the virialization of structure saturates the backreaction effect at the same level independently of the equality scale. This implies that backreaction is a small effect independently of initial conditions. Nevertheless, it may still contribute at the percent level to certain cosmological observables and therefore it cannot be neglected in precision cosmology.