Primordial nucleosynthesis as a probe of fundamental physics parameters

We analyze the effect of variation of fundamental couplings and mass scales on primordial nucleosynthesis in a systematic way. The first step establishes the response of primordial element abundances to the variation of a large number of nuclear physics parameters, including nuclear binding energies. We find a strong influence of the $n-p$ mass difference (for the ${}^4\mathrm{He}$ abundance), of the nucleon mass (for deuterium), and of $A=3$, 4, 7 binding energies (for ${}^3\mathrm{He}$, ${}^6\mathrm{Li}$, and ${}^7\mathrm{Li}$). A second step relates the nuclear parameters to the parameters of the standard model of particle physics. The deuterium, and, above all, ${}^7\mathrm{Li}$ abundances depend strongly on the average light quark mass $\widehat{m}\equiv (m_u+m_d)/2$. We calculate the behavior of abundances when variations of fundamental parameters obey relations arising from grand unification. We also discuss the possibility of a substantial shift in the lithium abundance while the deuterium and ${}^4\mathrm{He}$ abundances are only weakly affected.

Figure 1

Variation of primordial abundances with $\alpha$ in three GUT scenarios. The curves with the smallest variations of abundances show the first scenario, GUT1. Curves with larger, positive slope of $Y_{{}^7\mathrm{Li}}$) and $Y_{\mathrm{H}{}^4\mathrm{e}}$ and negative slope of $Y_{\mathrm{H}{}^3\mathrm{e}}$ and $Y_{\mathrm{D}}$ show the second, GUT2. Curves with larger, negative slope of $Y_{{}^7\mathrm{Li}}$) and $Y_{\mathrm{H}{}^4\mathrm{e}}$ and positive slope of $Y_{\mathrm{H}{}^3\mathrm{e}}$ and $Y_{\mathrm{D}}$ show the third, GUT3. Highlighted regions give the observational $1\sigma$ limits. Error bars indicate the standard BBN abundances with theoretical $1\sigma$ error [80], for three different values of $\eta$ about the WMAP central value, as indicated on the upper horizontal axis.

Figure 2

Variation of primordial abundances with $\alpha$ in three GUT scenarios including nonlinear effects. Labels as in Fig. 1.