# Primordial Gravitational Waves Spectrum in the Coupled-Scalar-Tachyon Bounce Universe

## TL;DR

This paper derives and analyzes the spectrum of primordial gravitational waves in a bounce universe model involving coupled scalar and tachyon fields, comparing it with inflationary predictions and discussing observational signatures.

## Contribution

It provides a detailed derivation of tensor perturbation equations in a coupled scalar-tachyon bounce universe and introduces matching conditions across the bounce.

## Key findings

- Gravitational wave spectrum exhibits distinct scale dependence from inflation.
- Matching conditions effectively connect pre- and post-bounce tensor modes.
- Potential observational signatures differentiate bounce universe from inflationary models.

## Abstract

We derive in detail the equations of motion for the tensorial modes of primordial metric perturbations in the Coupled-Scalar-Tachyon Bounce Universe. We solve for the gravitational wave equations in the pre-bounce contraction and the post-bounce expansion epochs. To match the solutions of the tensor perturbations, we idealise the bounce process yet retaining the essential physical properties of the bounce universe. We put forward two matching conditions: one ensures the continuity of the gravitational wave functions and the other respects the symmetric nature of the bounce dynamics. The matching conditions connect the two independent modes of gravitational waves solutions before and after the bounce. We further analyse the scale dependence and time dependence of the gravitational waves spectra in the bounce universe and compare them with the primordial spectrum in the single field inflation scenario. We discuss the implications to early universe physics and present model independent observational signatures extracted from the bounce universe.