Gravitational Theory with a Dynamical Time

Abstract

A gravitational theory involving a vector field ${\chi }^{\mu }$, whose zero component has the properties of a dynamical time, is studied. The variation of the action with respect to ${\chi }^{\mu }$ gives the covariant conservation of an energy momentum tensor $T_{(\chi )}^{\mu \nu }$. Studying the theory in a background which has killing vectors and killing tensors we find appropriate shift symmetries of the field ${\chi }^{\mu }$ which lead to conservation laws. The energy momentum that is the source of gravity $T_{(G)}^{\mu \nu }$ is different but related to $T_{(\chi )}^{\mu \nu }$ and the covariant conservation of $T_{(G)}^{\mu \nu }$ determines in general the vector field ${\chi }^{\mu }$. When $T_{(\chi )}^{\mu \nu }$ is chosen to be proportional to the metric, the theory coincides with the Two Measures Theory, which has been studied before in relation to the Cosmological Constant Problem. When the matter model consists of point particles, or strings, the form of $T_{(G)}^{\mu \nu }$, solutions for ${\chi }^{\mu }$ are found. For the case of a string gas cosmology, we find that the Milne Universe can be a solution, where the gas of strings does not curve the spacetime since although $T_{(\chi )}^{\mu \nu }\ne 0$, $T_{(G)}^{\mu \nu }=0$, as a model for the early universe, this solution is also free of the horizon problem. There may be also an application to the "time problem" of quantum cosmology.

21 pages, discussions extended, some more explicit proofs included, more references included

References in corpus (7)

• Fine Tuning Free Paradigm of Two Measures Theory: K-Essence, Absence of Initial Singularity of the Curvature and Inflation with Graceful Exit to Zero Cosmological Constant State
• Exotic Low Density Fermion States in the Two Measures Field Theory: Neutrino Dark Energy
• Absence of the Fifth Force Problem in a Model with Spontaneously Broken Dilatation Symmetry
• Universes out of almost empty space
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• Analysis of Rotation Curves in the Framework of the Gravitational Suppression Model
• A Way to Dynamically Overcome the Cosmological Constant Problem

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• Unified Dark Energy and Dark Matter from Dynamical Space Time
• Unification of DE-DM from Diffusive Cosmology
• Dark energy and dark matter unification from dynamical space time: observational constraints and cosmological implications
• Non-Canonical Volume-Form Formulation of Modified Gravity Theories and Cosmology
• A transition between bouncing hyper-inflation to ΛCDM from diffusive scalar fields
• Linear potentials in galaxy halos by Asymmetric Wormholes
• Non Singular Origin of the Universe and its Present Vacuum Energy Density
• Unified Dark Energy and Dark Matter from Dynamical Spacetime Cosmology
• Inflaton as a pseudo-Goldstone boson of vacuum energy shift symmetry