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arXiv · 2012.09158

Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario

M. F. Gusson·A. Oakes O. Gonçalves·R. G. Furtado·J. C. Fabris·J. A. Nogueira
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Abstract

In this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $[\hat{X},\hat{P}] := \frac{i\hbar}{ 1 - β\hat{P}^2 }$ . We determine the wave function of the Universe $ ψ_{qp}(ξ,t)$, which is solution of the modified Wheeler-DeWitt equation in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although $ψ_{qp}(ξ,t)$ is a physically acceptable state it is not a realizable state of the Universe because $ ψ_{qp}(ξ,t)$ has infinite norm, as in the ordinary case with no minimal length.

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M. F. Gusson, A. Oakes O. Gonçalves, R. G. Furtado, J. C. Fabris, J. A. Nogueira. 2021-04-05. Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario. https://doi.org/10.1140/epjc%2Fs10052-021-09114-8

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