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We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert (devoid of local degrees of freedom) perfect fluid having an equation of state with a constant parameter $w$. For the range of $w$ near $-1$ this dark fluid can play the role of dark energy, while for $w=0$ this dark dust admits spatial inhomogeneities and can be interpreted as dark matter. We discuss possible implications of this model in the cosmological initial conditions problem. In particular, this is the extension of known microcanonical density matrix predictions for the initial quantum state of the closed cosmology to the case of spatially open Universe, based on the imitation of the spatial curvature by the dark fluid density. We also briefly discuss quantization of this model necessarily involving the method of gauge systems with reducible constraints and the effect of this method on the treatment of recently suggested mechanism of vacuum energy sequestering.
The recently suggested generalized unimodular gravity theory, which was originally put forward as a model of dark energy, can serve as a model of cosmological inflation driven by the effective perfect fluid -- the dark purely gravitational sector of
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by mea
Adopting Diracs brane variation prescription, the energy-momentum tensor of a brane gets supplemented by a geometrical (embedding originated) dark component. While the masslessness of the graviton is preserved, and the Newton force law is recovered,
We consider modifications of general relativity characterized by a special noncovariant constraint on metric coefficients, which effectively generates a perfect-fluid type of matter stress tensor in Einstein equations. Such class of modified gravity
We analyse the emergent cosmological dynamics corresponding to the mean field hydrodynamics of quantum gravity condensates, in the tensorial group field theory formalism. We focus in particular on the cosmological effects of fundamental interactions,