On the phantom barrier crossing and the bounds on the speed of sound in non-minimal derivative coupling theories

Israel Quiros, Tame Gonzalez, Ulises Nucamendi, Ricardo Garcia-Salcedo, Francisco Antonio Horta-Rangel, Joel Saavedra

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


In this paper we investigate the so-called 'phantom barrier crossing' issue in a cosmological model based on the scalar-tensor theory with non-minimal derivative coupling to the Einstein tensor. Special attention will be paid to the physical bounds on the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based on the non-minimal derivative coupling theory - this includes both the quintessence and the pure derivative coupling cases - has serious causality problems related to superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite the fact that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that, independent of the self-interaction potential, for positive coupling the tensor perturbations propagate superluminally, while for negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation.

Original languageEnglish
Article number075005
JournalClassical and Quantum Gravity
Issue number7
StatePublished - 28 Feb 2018


  • causality
  • gradient instability
  • phantom barrier crossing
  • scalar perturbations
  • scalar-tensor theory
  • squared sound speed
  • tensor perturbations


Dive into the research topics of 'On the phantom barrier crossing and the bounds on the speed of sound in non-minimal derivative coupling theories'. Together they form a unique fingerprint.

Cite this