General theory of cosmological perturbations in open and closed universes from the Horndeski action

Shingo Akama, Tsutomu Kobayashi

Published 2018-10-03Version 1

Our Universe is nearly spatially flat, but this does not mean that it is exactly spatially flat. In this paper we derive general quadratic actions for cosmological perturbations in non-flat models from the Horndeski theory. This allows us to study how the spatial curvature influences the behavior of cosmological perturbations in the early universe described by some general scalar-tensor theory. We show that a tiny spatial curvature at the onset of inflation is unlikely to yield large (or ${\cal O}(1)$) effects on the primordial spectra even if one modifies gravity. We also argue that non-singular cosmological solutions in the Horndeski theory are unstable in spatially open cases as well as in flat cases.