Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings in Canonical and Minimally Coupled Scalar Field and Possible Solutions in k-Essence Models

Abstract

General relativity has its successes at the local astrophysical level, however, it seems to be insufficient in describing the Universe at large scales. In this work, we investigate how the generalized scalar field theories in the context of general relativity can accommodate a phantom-to-quintessence transition, which may be an essential element of realistic Dark Energy scenarios in the late Universe. As we demonstrate in a very detailed manner, this is impossible for a canonical and minimally coupled single scalar field theory, but it may be possible for $k$-essence theories. We point out how the ghost instabilities may be eliminated, and we analyze the quantitative features of a $k$-essence theory that may realize a phantom-to-quintessence transition in the late Universe. We also qualitatively compare the difficulties and fine-tunings required for $k$-essence theories to realize a phantom-to-quintessence transition, and how such a transition is naturally realized in modified gravity, without unnecessary fine-tunings and ghost eliminations.