Big Bang Nucleosynthesis as a Probe of First-Order Phase Transitions
Supercooled cosmological first-order phase transitions (FOPTs) generate a large temperature inhomogeneity due to their stochastic reheating process. If a baryon asymmetry production predates the FOPT and is conserved during it, the temperature contrast is transferred onto the baryon-to-photon ratio $η$ or the baryon-to-entropy ratio $Y_{B}$, producing an inhomogeneity probed by big bang nucleosynthesis (BBN). We extend a recent formalism for this effect by including the reheating dependence of the induced $Y_{B}$ fluctuations, combining the transition-time power spectrum from finite-bubble statistics with proton and neutron diffusion at the BBN epoch. When the nucleation temperature is in the range $10^{-2}\,{\rm GeV} \lesssim T_{n} \lesssim 10^{2}\,{\rm GeV}$, the precise measurement of deuterium abundances disfavors parameter regions with a sizable latent heat and a long transition duration at the $1 σ$ level. The bound weakens towards higher $T_{n}$ as diffusion becomes more efficient. We further show that this bound disfavors FOPT parameter regions compatible with the NANOGrav gravitational wave signal. This conclusion assumes that the baryon asymmetry predates the transition and that the fluctuation spectrum remains valid down to sub-bubble scales. Therefore, in such FOPT explanations of the NANOGrav signal, the baryon asymmetry cannot simply predate the transition. It can instead be generated after reheating or during the transition if the local baryon production tracks the local entropy injection. As a result, the timing of baryogenesis may be constrained by combining gravitational wave observations with light element abundance measurements.