Gravitational Wave Constraints on the Bouncing Energy Scale of Big Bounce Cosmology

TL;DR

This paper establishes a relation between the bouncing energy scale in big bounce cosmology and the gravitational wave background, using detector sensitivities to constrain models and identify detectable signals.

Contribution

It provides the first systematic gravitational wave constraint on the bouncing energy scale and analyzes the parameter space where big bounce models can produce detectable signals.

Findings

Current SGWB searches exclude certain contraction-phase equations of state.

No detectable SGWB for specific parameter ranges with low bouncing energy scale.

A window exists where a detectable SGWB can be produced, favoring matter-dominated contraction models.

Abstract

Big bounce cosmology provides a solution to the Universe's initial singularity, and stochastic gravitational wave background (SGWB) searches offer a promising avenue for testing this paradigm. In this work, we establish an analytical relation between the bouncing energy scale, $\rho_{s\downarrow}^{1/4}$, and SGWB spectrum, $\Omega_\mathrm{GW}(f)h^2$, for big bounce cosmology. By combining sensitivities from major GW detectors (e.g., Planck/BICEP, PTA, and LIGO/Virgo across low, medium, and high frequencies, respectively), we provide the first systematic GW constraint on $\rho_{s\downarrow}^{1/4}$. Our results show that the region $-\tfrac{1}{3} < w_1 < -0.17$ is excluded by current SGWB searches, given the constraint $\rho_{s\downarrow}^{1/4} > 1~\mathrm{TeV}$, where $w_1$ is the contraction-phase equation of state parameter. Additionally, no detectable SGWB can be generated for $0.038 < w_1 < \infty$ with $\rho_{s\downarrow}^{1/4} < 10^{16}~\mathrm{TeV}$. We identify a window, $-0.17 < w_1 < 0.038$, in which a detectable SGWB can be produced, disfavoring nearly all big bounce models except for the matter-dominated contraction model ($w_1 \simeq 0$).