Quantifying the sensitivity of Big Bang Nucleosynthesis to isospin
  breaking with input from lattice QCD
  We perform the first quantitative study of the sensitivity of Big Bang
Nucleosynthesis to variations in isospin breaking with precise input from
lattice QCD calculations. The predicted light nuclear abundances are most
sensitive to the neutron-proton mass splitting as both the initial relative
abundance of neutrons to protons and the $n \rightleftharpoons p$ weak reaction
rates are very sensitive to this quantity. Lattice QCD has been used to
determine this mass splitting to greater than 5-sigma, including contributions
from both the down-quark up-quark mass splitting, $2\delta = m_d-m_u$ and from
electromagnetic coupling of the quarks to the photons with a strength governed
by the fine structure constant, $\alpha_{fs}$. At leading order in isospin
breaking, the contribution of $\delta$ and $\alpha_{fs}$ to $M_n-M_p$ and the
nuclear reaction rates can be varied independently. We use this knowledge and
input from lattice QCD to quantitatively study variations of the predicted
light nuclear abundances as $\delta$ and $\alpha_{fs}$ are varied. The change
in the D and ${}^4$He abundances individually allow for potentially large
simultaneous variations in $\delta$ and $\alpha_{fs}$ while maintaining
consistency with the observed abundances, however the combined comparison
restricts variations in these sources of isospin breaking to less than
$\lesssim1.25\%$ at the 3-sigma confidence level. This sensitivity can be used
to place tight constraints on prospective beyond the Standard Model theories
that would modify these isospin breaking effects in the primordial Universe.
