Viability of nonminimally coupled $$f\,(R)$$ f ( R ) gravity

Abstract

In this work we explore the viability of nonminimally coupled mattercurvature gravity theories, namely the conditions required for the absence of tachyon instabilities and ghost degrees of freedom. We contrast our finds with recent claims of a pathological behaviour of this class of models, which resorted to, in our view, an incorrect analogy with k-essence.

A note on viability of nonminimally coupled f(R) theory

“…That this redefinition is always possible renders the concerns of Ref. [6] moot, in particular we do not find a "more complex dependency of the putative k-essence function p on φ" that is "much more evolved than assumed". In the Appendix (1) we explicitly derive, from the action (1), the equivalent action (2).…”

“…The latter point of view was not taken in the recently published paper [6], where it was argued e.g. that the constraints do not apply to "models in which there is only baryonic matter" and that "faster-than-light propagation of perturbations for a particular matter species does not invalidate the underlying theory, but instead shows that the adopted matter content is unphysical".…”

“…Ref. [6] was, however, further concerned that the constraints presented in Ref. [5] might not be applicable even in the casê L =X = − 1 2ĝ αβ ψ ,α ψ ,β .…”

“…The purpose of this note is to clarify the issues that were raised in Ref. [6], detailing some steps omitted in the original derivations of Ref. [5].…”

“…Let us begin by quoting the action (1) rewritten in the Einstein frame (which we here denote with the "unhatted" geometric variables) as the following two-scalar theory (cf. (15) of [5] and (27) of [6]) :…”