Generalized multi-Galileons, covariantized new terms, and the no-go theorem for nonsingular cosmologies

Abstract

It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that they do not participate in the no-go argument.

A covariant Lagrangian for stable nonsingular bounce

“…Based on the effective field theory (EFT) of nonsingular cosmologies [8][9][10], this No-go result has been more clearly illustrated. It is found that the stable nonsingular cosmological models can be implemented only in the theories beyond cubic Galileon, (see also [11,12]). …”

Cuscuton gravity as a classically stable limiting curvature theory

“…However, one has to be slightly careful with certain limits. For example, taking the UV limit of action (45) yields…”

Higher order derivative coupling to gravity and its cosmological implications

“…As was first found in [20] (see also [21]), the R (3) δg 00 operator plays a crucial role in solving the gradient instability problem induced by c 2 s < 0, (see also [30] for the unitarity problem), which suffered by the nonsingular cosmologies based on the Horndeski theory [23] [24][31] [32].…”