Dark Energy from structure: a status report

Abstract

The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein's theory, restricting attention to scalar variables, this evolution can be modeled by solutions of a set of Friedmann equations for an effective volume scale factor, with matter and backreaction source terms. The latter can be represented by an effective scalar field ('morphon field') modeling Dark Energy.The present work provides an overview over the Dark Energy debate in connection with the impact of inhomogeneities, and formulates strategies for a comprehensive quantitative evaluation of backreaction effects both in theoretical and observational cosmology. We recall the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of challenges and unresolved issues in connection with their observational interpretation.The present status of this subject is intermediate: we have a good qualitative understanding of backreaction effects pointing to a global instability of the standard model of cosmology; exact solutions and perturbative results modeling this instability lie in the right sector to explain Dark Energy from inhomogeneities. It is fair to say that, even if backreaction effects turn out to be less important than anticipated by some researchers, the concordance high-precision cosmology, the architecture of current N-body simulations, as well as standard perturbative approaches may all fall short in correctly describing the Late Universe. Keywords

Averaged Lemaître–Tolman–Bondi dynamics

“…According to [20], kinematic backreaction and averaged curvature may be interpreted in terms of an effective backreaction fluid by (the subindex b denotes backreaction)…”

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

“…Also in the back-reaction approach [107,108] to cosmology, according to which dark energy is a byproduct of the non-linearities of GR when one considers spatial averages of 3-scalar quantities in the 3-spaces on large scales to get a cosmological description of the universe taking into account its observed inhomogeneity, one gets that the spatial average of the product of the lapse function and of the York time (a 3-scalar gauge variable) gives the effective Hubble constant. Since this approach starts from the Hamiltonian description of an asymptotically flat space-time and since all the canonical variables in the York canonical basis, except the angles θ i , are 3-scalars, the formalism presented in this Lecture will allow to study the spatial average of nearly all the Hamilton equations and not only of the super-Hamiltonian constraint and of the Hamilton equation for the York time as in the existing formulation of the approach.…”

Cosmology and fundamental physics

“…There also is the interesting idea that the backreaction of density inhomogeneities on the expansion may produce the measured effect of an accelerated cosmic expansion [3].…”