Primordial Gravitational Waves of Big Bounce Cosmology in Light of Stochastic Gravitational Wave Background

TL;DR

This paper analytically studies primordial gravitational waves in big bounce cosmology, categorizing scenarios into four types, and explores their implications for interpreting stochastic gravitational wave background signals detected by pulsar timing arrays and future detectors.

Contribution

It provides an analytical framework for primordial gravitational wave spectra in big bounce cosmology, applicable to various models with constant equation of state in each phase.

Findings

Identifies four distinct categories of big bounce scenarios based on gravitational wave evolution.

Derives explicit analytical solutions for the primordial gravitational wave spectrum in these scenarios.

Suggests applications of the results to current and future gravitational wave observations for cosmological insights.

Abstract

Primordial gravitational waves from the very early stages of the universe, such as inflation or bounce processes, are an irreducible cosmological source of the stochastic gravitational wave background (SGWB). The recent detection of SGWB signals around the nano-Hertz frequency by pulsar timing arrays (PTAs), including NANOGrav, EPTA, PPTA, IPTA, and CPTA, opens a new window to explore these very early stages of the universe through these primordial gravitational waves. In this work, we investigate the generation and evolution of primordial gravitational waves in a generic big bounce cosmology by parameterizing its background evolution into four phases, where perturbation modes exit and re-enter the horizon twice. By analytically solving the equation of motion for primordial gravitational waves and matching solutions at the boundaries, we obtain the explicit form of the primordial gravitational wave spectrum in a generic big bounce cosmology. We find that, according to the evolution of primordial gravitational waves, a generic scenario of big bounce cosmology can be categorized into four distinct types. We introduce four toy models for these categories, demonstrating that our analytical results can be straightforwardly applied to various bouncing universe models in which the equation of state of the background is constant in each phase. We also prospect future applications of our results in interpreting SGWB signals searched by PTAs and upcoming advanced gravitational wave detectors such as SKA, Taiji, Tianqin, LISA, DECIGO, and aLIGO/Virgo/KAGRA using Bayesian analysis.