Big Bang Nucleosynthesis Confronts Domain Walls and First-Order Phase Transitions as the Pulsar Timing Array Explanations

Pulsar timing arrays (PTAs) have detected a nanohertz gravitational-wave background, often attributed to annihilating domain walls (DWs) or first-order phase transitions (FOPTs). Their reheating imprints fluctuations in the baryon-to-photon ratio. These so-called baryon isocurvature fluctuations $S_B$ survive until Big Bang Nucleosynthesis, whose yields depend nonlinearly on it. Modest $S_B$ fluctuations can therefore alleviate the current deuterium tension in parts of the PTA preferred regions and therefore strengthen their interpretation. Overabundant DWs and too strong FOPTs overproduce $D\mathrm{/}H$ and are ruled out.