Determine the impact of turbulence cascading to the nucleon diffusion scale

Determine how turbulence induced by moving domain walls during domain-wall annihilation or by bubble walls during a first-order phase transition, if it cascades to the nucleon diffusion scale, affects the baryon-isocurvature constraints and Big Bang nucleosynthesis findings.

Background

The paper derives Big Bang nucleosynthesis constraints on domain-wall and first-order phase-transition interpretations of the pulsar-timing-array gravitational-wave background through baryon-isocurvature fluctuations generated by inhomogeneous reheating. These constraints assume that the source-induced baryon inhomogeneity is treated using the relevant diffusion scales and that additional plasma dynamics do not significantly alter the spatial structure before nucleosynthesis.

The authors note that the moving walls associated with domain-wall annihilation and first-order phase transitions generate bulk plasma motion. If the resulting turbulence cascades to the nucleon diffusion scale, it could modify neutron and proton transport and consequently change the surviving baryon inhomogeneity and its imprint on primordial deuterium. The quantitative effect of this process is not evaluated in the paper and is explicitly deferred to future work.

References

Finally, the moving walls that source the GW signal, during either DW annihilation or FOPT, also induce bulk motion of the plasma. The resulting turbulence could cascade down to the nucleon diffusion scale, and we leave its impact on our findings to future work.

— Big Bang Nucleosynthesis Confronts Domain Walls and First-Order Phase Transitions as the Pulsar Timing Array Explanations  (2609.25950 - Elahi et al., 22 Sep 2026) in Discussion and conclusion