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The Avoidance of the Little Sibling of the Big Rip Abrupt Event by a Quantum Approach

A. Alecu, I. Albarran, M. Bouhmadi-López, F. T. O. Cabral, P. Martín-Moruno

We address the quantisation of a model that induces the Little Sibling of the Big Rip (LSBR) abrupt event, where the dark energy content is described by means of a phantom-like fluid or a phantom scalar field. The quantisation is done in the framework of the Wheeler–DeWitt (WDW) equation and imposing the DeWitt boundary condition; i.e., the wave function vanishes close to the abrupt event. We analyse the WDW equation within two descriptions: First, when the dark energy content is described with a perfect fluid. This leaves the problem with the scale factor as the single degree of freedom. Second, when the dark energy content is described with a phantom scalar field in such a way that an additional degree of freedom is incorporated. Here, we have applied the Born–Oppenheimer (BO) approximation in order to simplify the WDW equation. In all cases, the obtained wave function vanishes when the LSBR takes place, thus fulfilling the DeWitt boundary condition.

dark energy; cosmological singularities; quantum cosmology

Volume 6, Number 1, Page 13
2018 February

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Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia