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The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the dynamics though correction (backreaction) terms, which can lead to behaviour qualitatively and quantitatively different from the Friedmann-Lema^{i}tre-Robertson-Walker models. The effects of averaging on cosmological observations are discussed. It is argued that, based on estimates from observational data, the backreaction (and, in particular, the averaged spatial curvature) can have a very significant dynamical effect on the evolution of the Universe and must be taken into account in observational cosmology.
We introduce a generalization of the 4-dimensional averaging window function of Gasperini, Marozzi and Veneziano (2010) that may prove useful for a number of applications. The covariant nature of spatial scalar averaging schemes to address the averag
In the Kaluza-Klein model with a cosmological constant and a flux, the external spacetime and its dimension of the created universe from a $S^s times S^{n-s}$ seed instanton can be identified in quantum cosmology. One can also show that in the intern
We develop a novel model for Cosmological Hyperfluids, that is fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity. Imposing the Cosmological Principle to Metric-Affine Spaces, we present the most general covariant for
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Uni
We derive a model of dark energy which evolves with time via the scale factor. The equation of state $omega=(1-2alpha)/(1+2alpha)$ is studied as a function of a parameter $alpha$ introduced in this model. In addition to the recent accelerated expansi