I will discuss the implications of precision measurements of light element abundances in concordance with the Cosmic Microwave Background for scenarios of physics beyond the Standard Model that generate large inhomogeneities in the baryon-to-photon ratio. I will show that precision Big Bang Nucleosynthesis (BBN) constrains mechanisms that produce large scale inhomogeneities at temperatures of the order or below a TeV. In particular, we see that inhomogeneities of the order of 25% at comoving lengths scales larger than the comoving horizon at the temperature of 3 TeV are in conflict with the measured light element abundances. This sensitivity to physics at such early times is because inhomogeneities in baryon number homogenize predominantly through diffusion, which is a slow process. BBN therefore acts as a novel probe of baryogenesis below the TeV scale, readily ruling out some proposed scenarios in the literature. I will discuss the implications for electroweak baryogenesis. In addition I will show that precision BBN is a new probe of first order phase transitions which produce a gravitational wave signal in the frequency range from pHz to mHz. This leads to constraints on the electroweak phase transition, as well as the first order phase transitions that have been postulated to explain the pulsar timing array signal. Finally, I will comment on the future prospects for improving this probe.
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