Does small scale structure significantly affect cosmological dynamics?

Abstract

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 virialisation 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.