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تسجيل مستخدم جديدDynamics of the generalized unimodular gravity theory
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The Hamiltonian formalism of the generalized unimodular gravity theory, which was recently suggested as a model of dark energy, is shown to be a complicated example of constrained dynamical system. The set of its canonical constraints has a bifurcation -- splitting of the theory into two branches differing by the number and type of these constraints, one of the branches effectively describing a gravitating perfect fluid with the time-dependent equation of state, which can potentially play the role of dark energy in cosmology. The first class constraints in this branch generate local gauge symmetries of the Lagrangian action -- two spatial diffeomorphisms -- and rule out the temporal diffeomorphism which does not have a realization in the form of the canonical transformation on phase space of the theory and turns out to be either nonlocal in time or violating boundary conditions at spatial infinity. As a consequence, the Hamiltonian reduction of the model enlarges its physical sector from two general relativistic modes to three degrees of freedom including the scalar graviton. This scalar mode is free from ghost and gradient instabilities on the Friedmann background in a wide class of models subject to a certain restriction on time-dependent parameter $w$ of the dark fluid equation of state, $p=wvarepsilon$. For a special family of models this scalar mode can be ruled out even below the phantom divide line $w=-1$, but this line cannot be crossed in the course of the cosmological expansion. This is likely to disable the generalized unimodular gravity as a model of the phenomenologically consistent dark energy scenario, but opens the prospects in inflation theory with a scalar graviton playing the role of inflaton.
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A ghost free massive deformation of unimodular gravity (UG), in the spirit of {em mimetic massive gravity}, is shown to exist. This construction avoids the no-go theorem for a Fierz-Pauli type of mass term in UG by giving up on Lorentz invariance. In
our framework, the mimetic degree of freedom vanishes on-shell.
We discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We show how to gauge fix the transverse part of the diffeomorphism and then further to fulfill the unimodular gauge. This process requir
es the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the transverse diffeomorphism. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then suggest to define the quantum theory of Unimodular Gravity (UG) by making Fourier transform of GR in the unimodular gauge with respect to the cosmological constant and slightly generalizing it. This suggests that the quantum theory of UG may describe the same theory as GR but the spacetime volume is fixed. We also discuss problems left in this formulation of UG.
It is a well known result that any formulation of unimodular gravity is classically equivalent to General Relativity (GR), however a debate exists in the literature about this equivalence at the quantum level. In this work, we investigate the UV quan
tum structure of a diffeomorphism invariant formulation of unimodular gravity using functional renormalisation group methods in a Wilsonian context. We show that the effective action of the unimodular theory acquires essentially the same form with that of GR in the UV, as well as that both theories share similar UV completions within the framework of the asymptotic safety scenario for quantum gravity. Furthermore, we find that in this context the unimodular theory can appear to be non--predictive due to an increasing number of relevant couplings at high energies, and explain how this unwanted feature is in the end avoided.
The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial expansions of the
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