Stability of nonsingular cosmologies in Galileon models with torsion. A no-go theorem for eternal subluminality

Abstract: Generic models in Galileons or Horndeski theory do not have cosmological solutions that are free of instabilities and singularities in the entire time of evolution. We extend this No-Go theorem to a spacetime with torsion. On this more general geometry the No-Go argument now holds provided the additional hypothesis that the graviton is also subluminal throughout the entire evolution. Thus, critically different for Galileons' stability on a torsionful spacetime, an arguably unphysical although arbitrarily short (deep UV) phase occurring at an arbitrary time, when the speed of gravity $(c_g)$ is slightly higher than luminal $(c)$, and by at least an amount $c_g\geq \,\sqrt{2}\,c $, can lead to an all-time linearly stable and nonsingular cosmology. As a proof of principle we build a stable model for a cosmological bounce that is almost always subluminal, where the short-lived superluminal phase occurs before the bounce and that transits to General Relativity in the asymptotic past and future.