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.

General covariant symmetric teleparallel cosmology

“…While the cosmology of metric teleparallel theories has been thoroughly discussed in the literature [22,23], symmetric teleparallel cosmology has only recently received growing attention. Particular attention has been devoted to cosmology in the f (Q) class of theories [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], or theories which couple (pseudo-)scalar fields to the nonmetricity [39,40]. These studies make use of the fact that around any point in spacetime there exist local coordinates in which the coefficients of the symmetric teleparallel connection vanish identically.…”

Accelerating expansion of the universe in modified symmetric teleparallel gravity

“…This situation is called coincident gauge and the covariant derivative ∇ α reduces to the partial one ∂ α . But in any other coordinate system in which this affine connection does not vanish, the metric evolution will be affected and result in a completely different theory [40,41]. Thus in the coincident gauge coordinate , we have…”

“…The first cosmological solutions in f (Q) gravity appear in References [28,29], while f (Q) cosmography and energy conditions can respectively be seen in [30,31]. Quantum cosmology have been studied for a power-law model [32]. Cosmological solutions and growth index of matter perturbations have been investigated for a polynomial functional form of f (Q) [33].…”

Bulk viscous fluid in symmetric teleparallel cosmology: theory versus experiment

“…This situation is called coincident gauge and the covariant derivative ∇ α reduces to the partial one ∂ α . But in any other coordinate system in which this affine connection does not vanish, the metric evolution will be affected and result in a completely different theory [58,59]. Thus in the coincident gauge coordinate , we have…”