Classical and quantum fate of the little sibling of the big rip in f(R) cosmology

Abstract

The Little Sibling of the Big Rip is a cosmological abrupt event predicted by some phantom cosmological models that could describe our Universe. When this event is approached the observable Universe and its expansion rate grow infinitely, but its cosmic derivative remains finite. In this work we have obtained the group of metric f (R) theories of gravity that reproduce this classical cosmological background evolution. Furthermore, we have considered the quantization of some of the resulting models in the framework of quantum geometrodynamics, showing that the DeWitt criterion can be satisfied. Therefore, as it also happens in General Relativity, this event may be avoided in f (R) quantum cosmology.

Classical and Quantum f(R) Cosmology: The Big Rip, the Little Rip and the Little Sibling of the Big Rip

“…This model has been already studied in the f (R) quantum geometrodynamics approach, see reference [90]. In the next part of this section, we not only review the conclusion there presented but also provide a different, less restrictive and more general, approximation when solving for the wave function.…”

“…For previous works on reconstruction techniques in f (R) gravity see, for instance, references [80][81][82][83][84][85][86]. See also references [87][88][89][90][91] for successful reconstruction of phantom DE-driven riplike events in metric f (R) theories of gravity.…”

“…Therefore, the DW criterion can only be a sufficient but not necessary criterion for the avoidance of singularities. This criterion has been successfully applied in several cosmological scenarios, see, e.g., references [65,66,[71][72][73]89,90,[115][116][117] among others.…”

“…being R a constant needed for the change of variables to be well-defined. There are different proposals among the existing literature for the value of this constant, see, for instance, references [75,[89][90][91]. In this work we adopt the convention discussed in reference [91], where R is defined as the value of the curvature scalar evaluated at some future scale factor a = a on which the description of the universe by means of DE only becomes appropriate.…”

“…Please note that from this definition it follows R > R , since the scalar curvature asymptotically approaches an increasing function with the expansion of the universe. For different definitions of R see references [75,89,90]. In these new variables, Equation (59) transforms into…”