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 behaviour 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.
Highlights
Recent observations of the expansion history of the Universe indicate that the Universe is presently undergoing a phase of accelerated expansion [1, 2]
What will result from our analysis is that the evolution of sub-Hubble perturbations leads to an instability of the perturbative expansion due to the presence of large contributions which depend on a combination of Newtonian and post-Newtonian terms. This instability indicates that the effective scale factor describing the dynamics of our local Hubble patch is fed by the evolution of inhomogeneities within the Hubble radius. This cross-talk between the small-scale dynamics and the effective average dynamics described by super-Hubble, or “zero”-mode, playing the role of FRW-like background might be the crucial ingredient of backreaction that can lead to cosmic acceleration without dark energy
One possible explanation of the observations is that the Universe is homogeneously filled with a fluid with negative pressure that counteracts the attractive gravitational force of matter fields
Summary
Recent observations of the expansion history of the Universe indicate that the Universe is presently undergoing a phase of accelerated expansion [1, 2]. What will result from our analysis is that the evolution of sub-Hubble perturbations leads to an instability of the perturbative expansion due to the presence of large contributions which depend on a combination of Newtonian and post-Newtonian terms This instability indicates that the effective scale factor describing the dynamics of our local Hubble patch is fed by the evolution of inhomogeneities within the Hubble radius. This cross-talk between the small-scale dynamics and the effective average dynamics described by super-Hubble, or “zero”-mode, playing the role of FRW-like background might be the crucial ingredient of backreaction that can lead to cosmic acceleration without dark energy. We present the main results of a fourth-order gradientexpansion technique
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