The Breathing Universe: 702_Testing Temporal Coherence Across PTA Consortia

This study presents the first cross-consortium test of deterministic temporal coherence in Pulsar Timing Array (PTA) data. Building on earlier work that identified a six-mode coherent structure in the NANOGrav 12.5-year dataset, we extend the analysis to include the European Pulsar Timing Array Data Release 2 (EPTA DR2) and the International Pulsar Timing Array Data Release 2 (IPTA DR2). Using a unified 60-day binning pipeline, inverse-variance residual weighting, multi-mode harmonic regression, Bayesian evidence comparison, and Hellings–Downs correlation analysis, we examine whether the temporal modes, long-term drift, and helical frequency–phase structure found in NANOGrav persist across independent PTA datasets. All three PTAs independently recover the same multi-mode structure, including two well-resolved modes at periods of ~12–17 years, a stable low-frequency drift component, and a distinctive helical organization of phases across frequencies. These features are inconsistent with stochastic red-noise processes, gravitational-wave backgrounds, or multi-source continuous-wave models, and instead point to a global, deterministic temporal signal present across the sky. Bayesian model selection strongly favours deterministic multi-mode models over red-noise or multi-source SMBHB models, with Bayes factors ranging from strong to decisive. Removing the deterministic modes strengthens the quadrupolar Hellings–Downs signature, demonstrating that coherent temporal modes coexist with, rather than replace, the stochastic gravitational-wave background. The results show that deterministic temporal coherence is a reproducible astrophysical phenomenon and provide observational support for models in which the effective flow of time contains small, multi-frequency global modulations. The findings are consistent with dynamic temporal-field frameworks such as the Breathing Universe Model (BUM), without requiring any specific theoretical interpretation. This work establishes deterministic temporal structure as a new class of PTA observable and outlines clear predictions for upcoming PTA datasets, including IPTA DR3, NANOGrav 15-year, and the SKA era.