Abstract
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.
Highlights
It can be said that the science of Cosmology was born with Einstein’s General Relativity (GR) at the beginning of the 20th century
The paper is outlined as follows: In Section 2, we present a review of the phantom model that induces the Little Sibling of the Big Rip (LSBR) abrupt event, where the dark energy content is described first with a phantom-like fluid, and, with a phantom scalar field
We address the task of quantising the system adopting different points of view; First, the simplest case which consists in describing the content with a phantom fluid, where the scale factor is the single degree of freedom
Summary
It can be said that the science of Cosmology was born with Einstein’s General Relativity (GR) at the beginning of the 20th century. Several works try to explain the current cosmological speed up invoking an exotic component in the Universe known as Dark Energy (DE) [5,6,7] where the ΛCDM model is the widely accepted paradigm given its remarkable success on fitting the observational data. This model brings certain theoretical problems such as the coincidence problem and the cosmological constant problem. The paper is outlined as follows: In Section 2, we present a review of the phantom model that induces the LSBR abrupt event, where the dark energy content is described first with a phantom-like fluid, and, with a phantom scalar field. The Big Rip singularity and the abrupt events of Little Rip and Little Sibling of the Big Rip, if and only if phantom matter is present
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