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

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 $-\frac{1}{3}<w_1<-0.17$ 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 ($w_1\simeq 0$).

15 pages, 5 figures