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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 averaging problem in relativistic cosmology is an important property that is implied by construction, but usually remains implicit. We employ here the approach of Gasperini et al. for two reasons. First, the formalism and its generalization presented here are manifestly covariant. Second, the formalism is convenient for disentangling the dependencies on foliation, volume measure, and boundaries in the averaged expressions entering in scalar averaging schemes. These properties will prove handy for simplifying expressions, but also for investigating extremal foliations and for comparing averaged properties of different foliations directly. The proposed generalization of the window function allows for choosing the most appropriate averaging scheme for the physical problem at hand, and for distinguishing between the role of the foliation itself and the role of the volume measure in averaged dynamic equations. We also show that one particular window function obtained from this generalized class results in an averaging scheme corresponding to that of a recent investigation by Buchert, Mourier and Roy (2018) and, as a byproduct, we explicitly show that the general equations for backreaction derived therein are covariant.
Why is the Universe so homogeneous and isotropic? We summarize a general study of a $gamma$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The aniso
No. In a number of papers Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects. In particular, they argue that the effect of inhomogeneities on av
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $epsi
The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einsteins equations that is coordinate-inde
We investigate the cosmological applications of new gravitational scalar-tensor theories, which are novel modifications of gravity possessing 2+2 propagating degrees of freedom, arising from a Lagrangian that includes the Ricci scalar and its first a