# Generalized multi-Galileons, covariantized new terms, and the no-go theorem for non-singular cosmologies

## TL;DR

This paper extends the no-go theorem for non-singular cosmologies to multi-scalar second-order theories, showing that new covariantized terms do not evade gradient instability issues.

## Contribution

It generalizes the no-go result to multi-Galileon theories and introduces covariant completions of recently proposed new terms, confirming their non-participation in avoiding instabilities.

## Key findings

- No-go theorem applies to multi-scalar theories.
- New covariantized terms do not circumvent gradient instabilities.
- Gradient instabilities are a generic feature of non-singular solutions.

## 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.