Dynamics of the generalized unimodular gravity theory

Abstract

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, $p=w\epsilon$. 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.

arXiv comment20 pages, no figures

References in corpus (27)

• Planck 2015 results. XIII. Cosmological parameters
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• An alternative to quintessence
• The Dynamics of General Relativity
• Phantom Energy and Cosmic Doomsday
• Disappearing cosmological constant in f(R) gravity
• Can dark energy evolve to the Phantom?
• Nonlocal Cosmology
• Planck 2015 results. XIV. Dark energy and modified gravity
• Null energy condition and superluminal propagation
• Quantum Gravity Slows Inflation
• Scale invariance, unimodular gravity and dark energy
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Canonical Quantization of Cosmological Perturbations in the One Bubble Open Universe
• Serendipitous discoveries in nonlocal gravity theory
• Can infrared gravitons screen $\Lambda$?
• Hidden Negative Energies in Strongly Accelerated Universes
• The path integral of unimodular gravity
• Classical and Quantum Dynamics of Higher-Derivative Systems
• Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
• Technically natural dark energy from Lorentz breaking
• Darkness without dark matter and energy -- generalized unimodular gravity
• Hamiltonian analysis of mimetic scalar gravity revisited
• New Weyl-invariant vector-tensor theory for the cosmological constant
• Searching for the Evidence of Dynamical Dark Energy
• On the canonical structure and extra mode of generalized unimodular gravity

Cited by in corpus (17)

• Losing the trace to find dynamical Newton or Planck constants
• A note on unfree gauge symmetry
• Inflation in generalized unimodular gravity
• Unfree gauge symmetry in the Hamiltonian formalism
• Generalized unimodular gravity as a form of k-essence
• Hamiltonian constraints and unfree gauge symmetry
• Gauge symmetry of unimodular gravity in Hamiltonian formalism
• Restricted Gauge Theory Formalism and Unimodular Gravity
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• Hamiltonian BFV-BRST Quantization for the Systems with Unfree Gauge Symmetry
• General method for including Stueckelberg fields
• Generalized unimodular gravity in Friedmann and Kantowski-Sachs universes
• Reducible gauge symmetry versus unfree gauge symmetry in Hamiltonian formalism
• Bi-gravity with a single graviton
• Higgs Inflation in Unimodular Gravity
• Revisiting cosmological diffusion models in Unimodular Gravity and the $H_0$ tension
• Linking the Baum-Hawking-Coleman Mechanism with Unimodular Gravity and Vilenkin's Probability Flux