Is $w \neq -1$ evidence for a dynamical dark energy equation of state ?

TL;DR

Future precise measurements of the dark energy equation of state parameter $w$ could strongly indicate dynamical dark energy if $w$ significantly differs from -1, but such models require fine-tuning.

Contribution

This paper demonstrates that detecting $w eq -1$ would be strong evidence for dynamical dark energy, despite the possibility of fine-tuned models mimicking constant $w$.

Findings

Models with $w eq -1$ and slow dynamics require fine-tuning.

Future constraints could rule out a cosmological constant if $w$ deviates from -1.

Detection of $w eq -1$ would strongly suggest dynamical dark energy.

Abstract

Current constraints on the dark energy equation of state parameter, $w$, are expected to be improved by more than one order of magnitude in the next decade. If $|w-1| \gsim 0.01$ around the present time, but the dark energy dynamics is sufficiently slow, it is possible that future constraints will rule out a cosmological constant while being consistent with a time-independent equation of state parameter. In this paper, we show that although models with such behavior can be constructed, they do require significant fine-tuning. Therefore, if the observed acceleration of the Universe is induced by a dark energy component, then finding $w \neq -1$ would, on its own, constitute very strong evidence for a dynamical dark energy equation of state.