Phase space structure of symmetric teleparallel theory of gravity

Abstract

The `Generalized Symmetric Teleparallel Gravity' (GSTG) does not admit diffeomorphic invariance, since the auxiliary field as well as the shift vector act as non-propagating dynamical variables carrying 1/2 degrees of freedom each. We show that in a minisuperspace model, which is devoid of the shift vector, the problem is alleviated for locally Lorentz invariant GSTG theory, and diffeomorphic invariance is established at least for one connection. However, the eerie structure of the Hamiltonian constructed even in the background of spatially flat isotropic and homogeneous Robertson-Walker space-time, can not be maneuvered. In contrast, the other two spatially flat connections containing an arbitrary time dependent function, doesn't admit non-linear extension to `Symmetric Teleparallel Equivalent to General Relativity (STEGR). We therefore construct the phase-space structure with three different spatially flat connections for the `Lorentz invariant' linear-scalar-vector-tensor GSTG action. Diffeomorphic invariance is established and the associated Hamiltonians are found to be well behaved for all the three cases.

22 pages, 0 figures

References in corpus (43)

• Planck 2018 results. X. Constraints on inflation
• Coincident General Relativity
• The teleparallel equivalent of general relativity
• Cosmology in $f(Q)$ geometry
• Teleparallel Gravity: From Theory to Cosmology
• f(T) Gravity and local Lorentz invariance
• Cosmological perturbations in f(T) gravity
• Accelerating universe from F(T) gravity
• f(T) gravity mimicking dynamical dark energy. Background and perturbation analysis
• Covariant formulation of f(Q) theory
• Bouncing Cosmology in f(Q) Symmetric Teleparallel Gravity
• Einsteinian cubic gravity
• Nonmetricity formulation of general relativity and its scalar-tensor extension
• On the covariance of teleparallel gravity theories
• Conformal symmetry and accelerating cosmology in teleparallel gravity
• Covariant formulation of scalar-torsion gravity
• Cosmological perturbations in modified teleparallel gravity models
• Cosmological Perturbation in f(T) Gravity Revisited
• Trace-anomaly driven inflation in $f(T)$ gravity and in minimal massive bigravity
• Constant-roll Inflation in $f(T)$ Teleparallel Gravity
• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• On the impact of $f(Q)$ gravity on the Large Scale Structure
• Late-time cosmology with phantom dark-energy in $f(Q)$ gravity
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Metric-affine Geometries With Spherical Symmetry
• On the viability of $f(Q)$ gravity models
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Accelerating cosmological models in $f(Q)$ gravity and the phase space analysis
• On the strong coupling of Einsteinian Cubic Gravity and its generalisations
• The effective field theory approach to the strong coupling issue in $f(T)$ gravity
• Scalar perturbations in $f(T)$ gravity using the $1+3$ covariant approach
• Dirac-Bergmann analysis and Degrees of Freedom of Coincident $f(Q)$-gravity
• General cosmological perturbations in teleparallel gravity
• Hamiltonian formulation of curvature squared action
• On the Viability of the Intermediate Inflation Scenario with $F(T)$ Gravity
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• Inflation with F(T) Teleparallel Gravity
• The geometrical meaning of the Weitzenböck connection
• ADM formulation and Hamiltonian analysis of Coincident General Relativity
• On the gravitational energy problem and the energy of photons
• Reconstructing modified and alternative theories of gravity
• Probing symmetric teleparallel gravity in the early universe

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