Spinor wave function of the Universe in non-minimally coupled varying constants cosmologies

Abstract

In this paper, we introduce a non-minimally coupled varying speed of light and varying gravitational constant cosmological toy model. Using the Eisenhart-Duval lifting method, we extend the original minisuperspace of the model and depict the evolution of the system in the presence of the potential term as a geometrical flow associated with the lifted metric. We write the Dirac-Wheeler-DeWitt equation, which solution is a spinor wave function of the Universe. Then we find the solution of the Dirac-Wheeler-DeWitt equation, which describes the emergence of two early universe-antiuniverse pairs that differ with the conserved quantity, which is an analog of the spin.

Dark Matter in the Milky Way as the F-Type of Vacuum Polarization

“…The solution J −i|k| ( √ 2λe α ) in the extended space is "an heir" of the mass shell solution 2 ; 1 − i|k|; − a 2 2γ ada = 1; thus, the limit γ → 0 is an analog of using δ(α − α 0 ) in (42) and tending α 0 → −∞.…”

“…It should be noted that in fact, the function v does not depend on the time η because Ĥ0 χ = 0 and D commutes with H 0 . Thus, the time evolution arises only due to function u, or more accurately, due to the presence of the Dirac delta function in (42).…”

Scalar Product for a Version of Minisuperspace Model with Grassmann Variables

“…It should be noted that in fact, the function v does not depend on the time η because Ĥ0 χ = 0 and D commutes with H 0 . Thus, the time evolution arises only due to function u, or more accurately, due to the presence of the Dirac delta function in (42). Thus, the scalar product (40) reduces to…”

“…For simplicity, the question about scalar products could be considered in a minisuperspace model example. Minisuperspace models represent examples of simple systems with constraints and are widely used [34][35][36][37][38][39][40][41][42][43] to understand the main features of gravity quantization. Without experimental data for the minisuperspace model, one would not be able to straightforwardly check different approaches to gravity quantization.…”

Scalar Product for a Version of Minisuperspace Model with the Grassmann Variables

“…For simplicity, the question about the scalar product could be considered on a minisuperspace model example. Minisuperspace models are widely used in QG [23][24][25][26] to understand the main features of gravity quantization and represents an example of a simple system with constraints. Without the experimental data for the minisuperspace model, one could not check different approaches to gravity quantization straightforwardly.…”