Is Phantom Divide Crossing in General Relativity Completely Impossible? Shortcomings and Possible Solutions

TL;DR

This paper examines the limitations of standard scalar field theories in achieving phantom-to-quintessence transitions in dark energy models within general relativity and explores alternative theories like $k$-essence and modified gravity as potential solutions.

Contribution

It demonstrates the impossibility of phantom-to-quintessence transitions in canonical scalar fields and proposes ghost condensate theories and modified gravity as viable alternatives.

Findings

Canonical scalar fields cannot realize phantom-to-quintessence transition.

$k$-essence theories can potentially realize the transition with ghost stability.

Modified gravity naturally allows the transition without fine-tuning.

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 most general field theories in the context of general relativity can accomodate a phantom-to-quintessence transition which may be 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 ghost condensate theories like $k$-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.