Abstract
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.
Highlights
Dark matter and dark energy phenomena form a dark side of modern precision cosmology and, represent an unprecedentedly rich playground for various modifications of general relativity (GR)
We suggest a Lorentz non-invariant generalization of the unimodular gravity theory, which is classically equivalent to general relativity with a locally inert perfect fluid having an equation of state with a constant parameter w
To UMG the gravitational dynamics of this fluid is characterized by an independent of space and time constant which is fixed by initial conditions
Summary
Dark matter and dark energy phenomena form a dark side of modern precision cosmology and, represent an unprecedentedly rich playground for various modifications of general relativity (GR). Theory corresponding to is invariant under spatial rotations, so that this is a minimal breakdown of Lorentz symmetry from O (1, 3) to O (3) Another reason to consider it is an interesting fact that at the classical level such a theory effectively incorporates a special type of matter source – dark fluid with a nonlinear (general barotropic) equation of state. In the particular case of a pressureless dust with w = 0, corresponding to N(γ ) = const, the density of this dust is characterized by a single function of spatial coordinates entirely fixed by the initial conditions, which can be interpreted as a model of inhomogeneous distribution of dark matter similar to the mechanism of mimetic model [14] We analyze this model at the classical level and show that on shell (without extra matter sources) it is equivalent to general relativity with this special type of perfect fluid. As that of the sequestering mechanism – the canonical version of the BV method [16], which might clarify acausality puzzles of this mechanism and extend it to noncompact spacetimes
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