Eur. Phys. J. C (2025) 85: 714
https://doi.org/10.1140/epjc/s10052-025-14428-y

Regular Article - Theoretical Physics

Probing the bounce energy scale in bouncing cosmologies with pulsar timing arrays

Department of Astronomy, Key Laboratory of Astroparticle Physics of Yunnan Province, School of Physics and Astronomy, Yunnan University, No.2 Cuihu North Road, 650091, Kunming, China

^a changhongli@ynu.edu.cn

Received: 2 May 2025
Accepted: 12 June 2025
Published online: 29 June 2025

Abstract

In this work, we constrain the bounce energy scale ${\rho }_{s\downarrow }^{1/4}$ in a generic bouncing-cosmology framework using the probable nanohertz stochastic gravitational-wave signal from NANOGrav 15-year, EPTA DR2, PPTA DR3, and IPTA DR2. A full Bayesian fit to the analytic stochastic-GW spectrum, for the first time, reveals two distinct posterior branches in $({\rho }_{s\downarrow }^{1/4},w_1)$: one near $w_1\approx 0.3$ and another at $w_1\gg 1$, where $w_1$ is the contraction-phase equation of state. We find that current PTA data strongly favor the bounce hypothesis over six conventional SGWB sources, while yielding smaller Bayes factors than its parent dual inflation–bounce scenario as the bounce scale is explicit. Both branches imply ${\rho }_{s\downarrow }^{1/4}>M_{\text{pl}}$, indicating a trans-Planckian probe. In particular, the $w_1\gg 1$ branch violates the dominant energy condition, motivating novel early-Universe physics. These results, confirmed by an accelerated machine learning approach, offer a rare observational window into UV completions of cosmology.