On Quantum Cosmology in Teleparallel Gravity

Abstract

A quantum cosmology in teleparallel gravity is presented in this article. Teleparallel gravity is used to perform such an analysis once in General Relativity (GR) the concept of gravitational energy is misleading preventing the establishment of a concise quantum cosmology. The Wheeler-DeWitt like equation is obtained using the Weyl quantization and the teleparallel expression of energy. * Electronic address: alexandre.

Noether charge and black hole entropy in teleparallel gravity

“…[58] for a more recent technical discussion on this last point). See also the works [59,60] and the references therein for recent progress on quantization and on quantum cosmology in TEGR. It is then not excluded that this work could also lead to a better understanding at the quantum level of black hole entropy and even help resolve some of the deepest issues posed by the latter.…”

Towards Energy Discretization in Quantum Cosmology

“…Therefore there should be two kinds of connections one changing the derivatives of Lorentz vectors, called spin connection ω µab , and another one that affects greek indices, Γ λ µν . Then by the condition ∇ µ e a ν = 0 which leads to ∂ µ e a ν −Γ λ µν e a λ +ω µ a b e b ν = 0, we get Γ λ µν = e aλ e b ν ω µab +e aλ ∂ µ e aν and as a consequence the usual definition of curvature tensor, [15,18]. The torsion tensor which is defined by T λ µν = Γ λ µν − Γ λ ν µ reads T a µν (e, ω) = ∂ µ e a ν − ∂ ν e a µ + ω µaν − ω νaµ .…”

“…, L M being the lagrangian density of matter fields and Σ abc defined as follows [15,18]. Performing a functional derivative in the Lagrangian density L with respect to the tetrads e aµ , the field equations read…”

“…Thus it is the natural procedure to be used on a quantum theory of gravitation. It should be pointed out that the immediate function with physical meaning that arises for such a procedure is the very gravitational energy-momentum in teleparallel gravity [17,18].…”

Towards energy discretization in quantum cosmology

“…Of course such a theory has to have implications on a QC. In this sense a first step was to use the gravitational energy of Friedman-Lemaitre-Robertson-Walker (FLRW) metric together with the Weyl quantization procedure to obtain an analogous Wheeler-DeWitt equation [18] .…”