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Register a new userCosmological backreaction and its dependence on spacetime foliation
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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-independent and only functionally depends on a metric. This formalism is applicable to general 3+1 foliations of spacetime for an arbitrary fluid with tilted flow. We clarify the dependence on spacetime foliation and argue that this dependence is weak in cosmological settings. We also introduce a new set of averaged equations that feature a global cosmological time despite the generality of the setting, and we put the statistical nature of effective cosmologies into perspective.
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We show how to provide suitable gauge invariant prescriptions for the classical spatial averages (resp. quantum expectation values) that are needed in the evaluation of classical (resp. quantum) backreaction effects. We also present examples illustrating how the use of gauge invariant prescriptions can avoid interpretation problems and prevent misleading conclusions.
Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological backreaction. Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.
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.
We present the results of computational gravitational backreaction on simple models of cosmic string loops. These results give us insight into the general behavior of cusps and kinks on loops, in addition to other features of evolution. Kinks are rounded off via an asymmetric and divergent correction to the string direction. The result is that cusps emerge in the place of kinks but the resulting smooth string section has a small amount of energy. Existing cusps persist, but quickly lose strength as backreaction removes energy from the string surrounding the cusp. Both kinks and cusps have their location in space shifted slightly with each oscillation.
By making a suitable generalization of the Starobinsky stochastic inflation, we propose a classical phase space formulation of stochastic inflation which may be used for a quantitative study of decoherence of cosmological perturbations during inflation. The precise knowledge of how much cosmological perturbations have decohered is essential to the understanding of acoustic oscillations of cosmological microwave background (CMB) photons. In order to show how the method works, we provide the relevant equations for a self-interacting inflaton field. For pedagogical reasons and to provide a link to the field theoretical case, we consider the quantum stochastic harmonic oscillator.
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