# Can non-minimal coupling restore the consistency condition in bouncing universes?

## TL;DR

This paper investigates how non-minimal couplings can restore the validity of the consistency condition for three-point functions in bouncing universe models, where it is typically violated due to growing perturbation amplitudes.

## Contribution

The study demonstrates that appropriate non-minimal couplings can re-establish the consistency condition in bouncing universes, extending its applicability beyond inflationary scenarios.

## Key findings

- Non-minimal couplings can restore the consistency condition in bouncing models.
- The violation of the condition is linked to the growth of perturbations near the bounce.
- Explicit example with tensor perturbations supports the main claim.

## Abstract

An important property of the three-point functions generated in the early universe is the so-called consistency condition. According to the condition, in the squeezed limit wherein the wavenumber of one of the three modes (constituting the triangular configuration of wavevectors) is much smaller than the other two, the three-point functions can be completely expressed in terms of the two-point functions. It is found that, while the consistency condition is mostly satisfied by the primordial perturbations generated in the inflationary scenario, it is often violated in the bouncing models. The validity of the consistency condition in the context of inflation can be attributed to the fact that the amplitude of the scalar and tensor perturbations freeze on super-Hubble scales. Whereas, in the bouncing scenarios, the amplitude of the scalar and tensor perturbations often grow rapidly as one approaches the bounce, leading to a violation of the condition. In this work, with the help of a specific example involving the tensor perturbations, we explicitly show that suitable non-minimal couplings can restore the consistency condition even in the bouncing models. We briefly discuss the implications of the result.