Probing the Bounce Energy Scale in Bouncing Cosmologies with Pulsar Timing Arrays

Abstract: In this work we constrain the bounce energy scale $\rho_{s\downarrow}^{1/4}$ in a generic framework of bouncing cosmologies using the nanohertz stochastic gravitational-wave background recently detected by pulsar timing arrays (NANOGrav 15-yr, EPTA DR2, PPTA DR3, IPTA DR2). A full Bayesian fit of the analytic SGWB spectrum for this bounce scenario reveals, for the first time, two distinct posterior branches in $(\rho_{s\downarrow}^{1/4},w_1)$: one near $w_1\approx0.3$ and one at $w_1\gg1$, where $w_1$ is the contraction phase equation of state. We find that the bouncing model attains larger Bayes factors against each of six conventional SGWB sources (SMBHBs, inflationary GWs, cosmic strings, domain walls, first order phase transitions, scalar induced GWs), demonstrating strong preference of current PTA data for the bounce hypothesis. Compared to the more generic dual inflation bounce scenario, the concrete bounce realization yields smaller Bayes factors, indicating that PTA measurements impose tighter constraints when the bounce scale is explicit. Moreover, the two posterior branches illuminate distinct theoretical frontiers. The right branch ($w_1\gg1$) violates the dominant energy condition (DEC), thereby providing direct empirical impetus for models with novel early Universe physics, e.g. ghost condensates, higher-derivative or modified gravity operators, and extra dimensional effects. Independently, both branches infer $\rho_{s\downarrow}^{1/4}$ above the Planck scale $M_\mathrm{pl}$, demonstrating that current PTAs already probe trans-Planckian regimes. Together, these findings offer a rare observational window into UV completions of cosmology. We further describe how normalizing flow based machine learning can accelerate such Bayesian analyses as PTA data volumes increase.