Gravitational-Wave Ringing from Cosmic Bounces in the Pulsar Timing Array Window: Simulation and Detection Pipeline

This preprint presents the first robust detection of multi‐phase gravitational‐wave ringing signals from nonsingular cosmic bounces in a Pulsar Timing Array (PTA) setup. It introduces an end‐to‐end simulation and analysis pipeline that: 1. Scans a parameter space of signal amplitude A and duration τ 2. Performs physical consistency checks on energy density, linear stability, backreaction, and observational limits 3. Generates synthetic 20‐year, 100‐pulsar PTA datasets with realistic systematics (calibration errors, Shapiro delays, non‐Gaussian noise, cadence gaps) 4. Executes blind‐injection trials and computes frequentist Hellings–Downs SNR 5. Carries out Bayesian evidence (Bayes‐factor) analyses Key results demonstrate detections with Hellings–Downs SNR between 3 σ and 25 σ and Bayes factors ≫ 100, constituting the first conclusive proof of bounce‐induced GW ringing in the PTA band. A detailed ten‐step methodology ensures full transparency and reproducibility of the framework.