This paper shows that the observed abundance of light elements made in the first minutes after the Big Bang can limit a class of early-universe events called supercooled first-order phase transitions (FOPTs). In such transitions, bubbles of a new low-energy phase form at random times, reheating some regions earlier than others. If the excess of matter over antimatter (the baryon asymmetry) was already in place before the transition and is conserved through it, those temperature differences turn into variations in the local baryon-to-photon or baryon-to-entropy ratios. Those variations leave a trace in Big Bang nucleosynthesis (BBN), the process that made the universe’s light elements, especially deuterium.

The author extends earlier work by adding two realistic effects. First, they include how reheating itself changes the size of the baryon-ratio fluctuations. Second, they use a form of the transition-time power spectrum that comes from counting a finite number of bubbles and then follow how protons and neutrons diffuse before and during BBN. Combining these ingredients, the paper checks how measured deuterium abundances respond to FOPT parameters such as the nucleation temperature, the released latent heat, and the transition duration.

The analysis focuses on transitions with nucleation temperatures between about 10^-2 and 10^2 GeV. In that range, precise deuterium data disfavors regions of parameter space where the phase transition releases a large latent heat and takes a long time to finish. The statistical strength quoted is about the 1-sigma level, and the constraints become weaker at higher nucleation temperatures because particle diffusion smooths out the baryon inhomogeneities before BBN can record them.

The result matters because it links two very different probes of the early universe. Gravitational waves from FOPTs are being searched for in pulsar timing arrays such as NANOGrav. The paper finds that, under its assumptions, some FOPT models that would explain the NANOGrav signal are disfavored by BBN abundance measurements. That means observations of light elements and gravitational waves together can help pin down when and how the baryon asymmetry arose.