On cosmic acceleration without dark energy

TL;DR

This paper investigates whether cosmic acceleration can arise from the backreaction of cosmological perturbations within general relativity, without invoking dark energy or modified gravity. Using the Buchert averaging framework, it derives effective Friedmann equations governed by the kinematical backreaction $Q_D$ and the mean spatial curvature $\langle R\rangle_D$, and explores how these terms can drive acceleration in a local Hubble patch. Through a gradient-expansion and renormalization-group analysis, it shows that super-Hubble modes contribute curvature-like effects that dilute into the background, while sub-Hubble modes introduce growing backreaction terms that render a perturbative treatment unstable, signaling the need for a non-perturbative description. Although these results do not provide a conclusive mechanism for the current acceleration, they highlight backreaction as a potentially significant factor in the Universe's expansion history and motivate non-perturbative approaches to quantify its observable consequences, offering an alternative angle on the dark energy problem.

Abstract

We elaborate on the proposal that the observed acceleration of the Universe is the result of the backreaction of cosmological perturbations, rather than the effect of a negative-pressure dark-energy fluid or a modification of general relativity. Through the effective Friedmann equations describing an inhomogeneous Universe after smoothing, we demonstrate that acceleration in our local Hubble patch is possible even if fluid elements do not individually undergo accelerated expansion. This invalidates the no-go theorem that there can be no acceleration in our local Hubble patch if the Universe only contains irrotational dust. We then study perturbatively the time behavior of general-relativistic cosmological perturbations, applying, where possible, the renormalization group to regularize the dynamics. We show that an instability occurs in the perturbative expansion involving sub-Hubble modes. Whether this is an indication that acceleration in our Hubble patch originates from the backreaction of cosmological perturbations on observable scales requires a fully non-perturbative approach.