Space-time slicing in Horndeski theories and its implications for
  non-singular bouncing solutions
  In this paper, we show how the proper choice of gauge is critical in
analyzing the stability of non-singular cosmological bounce solutions based on
Horndeski theories. We show that it is possible to construct non-singular
cosmological bounce solutions with classically stable behavior for all modes
with wavelengths above the Planck scale where: (a) the solution involves a
stage of null-energy condition violation during which gravity is described by a
modification of Einstein's general relativity; and (b) the solution reduces to
Einstein gravity both before and after the null-energy condition violating
stage. Similar considerations apply to galilean genesis scenarios.
