Is Dark Energy Simulated by Structure Formation in the Universe ?

Abstract

The standard model of cosmology assumes that the Universe can be described to hover around a homogeneous-isotropic solution of Einstein's general theory of relativity. This description needs (sometimes hidden) hypotheses that restrict the generality, and relaxing these restrictions is the headline of a new physical approach to cosmology that refurnishes the cosmological framework. Considering a homogeneous geometry as a template geometry for the in reality highly inhomogeneous Universe must be considered a strong idealization. Unveiling the limitations of the standard model opens the door to rich consequences of general relativity, giving rise to effective (i.e. spatially averaged) cosmological models that may even explain the longstanding problems of dark energy and dark matter. We explore in this talk the influence of structure formation on average properties of the Universe by discussing: (i) general thoughts on why considering average properties, on the key-issue of non-conserved curvature, and on the global gravitational instability of the standard model of cosmology; (ii) the general set of cosmological equations arising from averaging the scalar parts of Einstein's equations, the generic property of structure formation interacting with the average properties of the Universe in a scale-dependent way, and the description of cosmological backreaction in terms of an effective scalar field.Before we discuss a more general cosmological framework within which we can understand inhomogeneity effects affecting global properties of world models, so-called backreaction effects, we put our heads together on a couple of general thoughts that lie at the basis of this framework. 1 Why averaging ?Cosmology is built on models for the evolution of space. Within the four-dimensional framework of general relativity we need to split the equations into spatial variables that evolve in a timedirection. Having set up such a foliation of space-time, we may select one that admits a global cosmological time, which labels spatial hypersurfaces to define a cosmological model [1,5]. As we observe structures in the Universe we look along the light-cone implying the need to relate observables to spatial distributions, in order to interpret them within a cosmological model. Within the standard model of cosmology, spatial fluctuations are conceived to evolve on an assumed background geometry that belongs to the class of FLRW (Friedmann-Lemaître-Robertson-Walker) cosmologies being homogeneous-isotropic solutions of Einstein's equations. However, the description of fluctuations only makes sense with respect to their spatial average distribution and its evolution: employing the standard model we implicitly assume that it reliably describes the evolution of the universal average. However, by deriving the spatial average distribution, which is homogeneous by construction and may be large-scale isotropic to comply with constraints from the observable Universe, we cannot confirm this hypothesis: a priori, the average does, in general, not evolve ...

Gauss–Bonnet–Chern approach to the averaged Universe

“…Many modeling assumptions for closure of the spatially averaged Einstein equations have been suggested (cf section 1.2) that respect (i) the generic coupling of geometry (curvature) to the sources also for the averaged variables, while in FLRW cosmology the impact of inhomogeneities on the global model is neglected, (ii) the generic non-conservation of the average scalar curvature [35], while in FLRW cosmology curvature is assumed to obey a conservation law, and (iii) the generic possibility of the change of sign of the averaged scalar curvature, being impossible in FLRW cosmology. There are show-cases that yield a natural and consistent explanation of (i) dark energy as a result of the coupling of structure formation to global properties of the universe model [33] and references therein, (ii) the coincidence problem, i.e. the fact that a dark energy component appears to become relevant for the universal expansion at the epoch of formation of nonlinear structures, (iii) a transition of positive initial curvature to a present-day negative curvature, (iv) the small matter density cosmological parameter found in local probes of the matter density, (v) the large angular diameter distance to the cosmic microwave background consistent with supernova constraints, and (vi) the local expansion rate measurements (removal of the 'Hubble tension'); for (i)-(vi) see the recent paper [64] and references therein.…”

Hubble Tension from Bubble Tension: Cosmic Voids, Local and Global Scales

“…While the supervoids are not only not completely empty, but also have a density of energy and evolution, and also because they are bulky, they are more likely to merge with each other and are much more suitable candidates for influence on the cosmic scales [13,14,16]. Therefore, the possibility of the role of these large inhomogeneities in the dynamics of the universe and the effects of their evolution in determining the value of cosmic parameters seems possible [17][18][19][20]. In the proposed hypothesis in [13], cosmic voids are assumed to be spherical bubbles.…”