Quantum Cosmology in $f(Q)$ theory

Abstract

We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann-Lemaître-Robertson-Walker spacetime in the context of $f(Q)$ cosmology. When the coincident gauge is considered, the resulting minisuperspace system possesses second class constraints. This distinguishes the quantization process from the typical Wheeler-DeWitt quantization, which is applied for cosmological models where only first class constraints are present (e.g. for models in General Relativity or in $f(R)$ gravity). We introduce the Dirac brackets, find appropriate canonical coordinates and then apply the canonical quantization procedure. We perform this method both in vacuum and in the presence of matter: a minimally coupled scalar field and a perfect fluid with a linear equation of state. We demonstrate that the matter content changes significantly the quantization procedure, with the perfect fluid even requiring to put in use the theory of fractional Quantum Mechanics in which the power of the momentum in the Hamiltonian is associated with the fractal dimension of a Lévy flight. The results of this analysis can be applied in $f(T)$ teleparallel cosmology, since $f(Q)$ and $f(T)$ theories have the same degrees of freedom and same dynamical constraints in cosmological studies.

arXiv commentLatex2e source file, 33 pages, 2 figures, accepted in CQG

References in corpus (56)

• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Fractional Schrodinger equation
• Modified teleparallel gravity: inflation without inflaton
• Coincident General Relativity
• Fractional Quantum Mechanics
• The Pre-Big Bang Scenario in String Cosmology
• Cosmology in $f(Q)$ geometry
• Teleparallel Gravity: From Theory to Cosmology
• Loop Quantum Cosmology
• The Area of a Rough Black Hole
• $f(Q,T)$ gravity
• String Cosmology: A Review
• The Cosmology of Modified Gauss-Bonnet Gravity
• A Short Review of Loop Quantum Gravity
• Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity
• First evidence that non-metricity f(Q) gravity could challenge $\Lambda$CDM
• Barrow holographic dark energy
• Teleparallel Palatini theories
• Energy Conditions in $f(Q)$ gravity
• Testing $F(Q)$ gravity with redshift space distortions
• Signatures of $f(Q)$-gravity in cosmology
• Accelerated Expansion of the Universe in Non-minimally Coupled Gravity
• Cosmography in $f(Q)$ gravity
• Quantum cosmology: a review
• Traversable wormhole geometries in $f(Q)$ gravity
• The generalized second law of thermodynamics with Barrow entropy
• Cosmic acceleration with bulk viscosity in modified $f(Q)$ gravity
• Translation of Einstein's Attempt of a Unified Field Theory with Teleparallelism
• Selection Rules in Minisuperspace Quantum Cosmology
• New observational constraints on $f(T)$ gravity through gravitational-wave astronomy
• Prospecting Black Hole Thermodynamics with Fractional Quantum Mechanics
• Constraining effective equation of state in $f(Q,T)$ gravity
• F(T) gravity and k-essence
• Scalar-torsion theories of gravity II: $L(T,X,Y,\varphi )$ theory
• de Sitter and Scaling solutions in a higher-order modified teleparallel theory
• Model parameters in the context of late time cosmic acceleration in $f(Q,T)$ gravity
• From Fractional Quantum Mechanics to Quantum Cosmology: An Overture
• Variational Principles in Teleparallel Gravity Theories
• Symmetry and Equivalence in Teleparallel Gravity
• Origin of classical structure from inflation
• Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities
• Broadening quantum cosmology with a fractional whirl
• Cosmology of $f(R,\square R)$ gravity
• Coordinate-Free Quantization of Second-Class Constraints
• Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
• $O(d,d)$ Symmetry in Quantum Cosmology
• Quantum cosmology of the multi-field scalar matter: some exact solutions
• No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology
• Class of solutions of the Wheeler-DeWitt equation with ordering parameter
• Probability of inflation in Loop Quantum Cosmology
• Minisuperspace Quantization of $f\left(T,B\right)$ Cosmology
• Quantization of the Szekeres System
• Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field
• Quantum mechanics allows setting initial conditions at a cosmological singularity: Gowdy model example
• Quantum string cosmology
• Quantization of Einstein-aether Scalar field Cosmology

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• Anisotropic nature of space-time in $f(Q)$ gravity
• Revisiting Cosmologies in Teleparallelism
• FLRW solutions in $f(Q)$ theory: the effect of using different connections
• Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in $f(Q)$ Gravity
• Forecasting constraints on deviations from general relativity in $f(Q)$ gravity with standard sirens
• On the viability of $f(Q)$ gravity models
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Crossing phantom divide in $f(Q)$ gravity
• Quintessence Behaviour of an Anisotropic Bulk Viscous Cosmological Model in Modified $f(Q)$-Gravity
• Anisotropic f(Q) gravity model with bulk viscosity
• Bianchi type-I Barrow holographic dark energy model in symmetric teleparallel gravity
• Cosmic jerk parameter in symmetric teleparallel cosmology
• Viscous fluid cosmology in symmetric teleparallel gravity
• Bulk viscous fluid in symmetric teleparallel cosmology: theory versus experiment