# Primordial Tensor Perturbation in Double Inflationary Scenario with a Break

## TL;DR

This paper investigates the effects of a break stage during double inflation on primordial tensor perturbations, finding that such a break generally suppresses the tensor power spectrum rather than enhancing it, especially when the EOS parameter is constant and greater than -1/3.

## Contribution

It demonstrates that intermediate break stages during inflation do not enhance tensor perturbations if the Hubble rate is non-increasing, clarifying the behavior of tensor spectra in double inflation models.

## Key findings

- Tensor spectrum is suppressed during break stages with constant EOS > -1/3.
- Oscillatory features in the spectrum are not enhanced, contrary to scalar perturbations.
- Suppression is due to correction terms beyond the leading order superhorizon solution.

## Abstract

We study the primordial tensor perturbation produced from the double inflationary scenario with an intermediate break stage. Because of the transitions, the power spectrum deviates from the vacuum one and there will appear oscillatory behavior. In the case of a scalar-type curvature perturbation, it is known that the amplitude of these oscillations may be enhanced to result in the power spectrum larger than the one for the vacuum case. One might expect the similar enhancement for the tensor perturbation as well. Unfortunately, it is found that when the equation of state (EOS) parameter $w=p/\rho$ of the break stage is a constant with $w>-1/3$, the amplitude of oscillations is never large enough to enhance the power spectrum. On the contrary, the power spectrum is found to be suppressed even on those scales that leave the horizon at the first inflationary stage and remain superhorizon throughout the entire stage. We identify the cause of this suppression with the correction terms in additional to the leading order constant solution on superhorizon scales. We argue that our result is general in the sense that any intermediate break stage during inflation cannot yield an enhancement of the tensor spectrum as long as the Hubble expansion rate is non-increasing in time.