A Discrete Primordial Gravitational-Wave Comb from Cyclic Universe Recondensation

We propose a novel primordial gravitational-wave (GW) signature arising from a cyclic cosmology anchored at the Quantum Chromodynamics (QCD) scale. The cosmological bounce, triggered by a vacuum condensate W, generates a discrete frequency comb due to the strict Tolman mass-scaling law between successive cycles. While the lowest-order harmonics of this comb map geometrically into the 1-60 nHz window of current Pulsar Timing Arrays (PTAs), a rigorous derivation of the phase transition dynamics from the scale-invariant effective potential yields a fast transition (beta/H > 500). This robustly shifts the energy peak of the comb into the 20-40 uHz band. Consequently, the model offers a mathematically strict null-result for the PTA signal (e.g., NANOGrav), instead providing a predictive falsifiable target for upcoming microhertz space interferometers like uAres.