Big bang nucleosynthesis with stable ${}^8\mathrm{Be}$ and the primordial lithium problem

A change in the fundamental constants of nature or plasma effects in the early universe could stabilize ${}^8\mathrm{Be}$ against decay into two ${}^4\mathrm{He}$ nuclei. Coc et al. examined the former effect on big bang nucleosynthesis as a function of $B_8$, the mass difference between two ${}^4\mathrm{He}$ nuclei and a single ${}^8\mathrm{Be}$ nucleus, and found no effects for $B_8\le 100\mathrm{keV}$. Here we examine stable ${}^8\mathrm{Be}$ with larger $B_8$ and also allow for a variation in the rate for ${}^4\text{He}+{}^4\text{He}\to {}^8\mathrm{Be}$ to determine the threshold for interesting effects. We find no change to standard big bang nucleosynthesis for $B_8<1\mathrm{MeV}$. For $B_8\gtrsim 1\mathrm{MeV}$ and a sufficiently large reaction rate, a significant fraction of ${}^4\mathrm{He}$ is burned into ${}^8\mathrm{Be}$, which fissions back into ${}^4\mathrm{He}$ when $B_8$ assumes its present-day value, leaving the primordial ${}^4\mathrm{He}$ abundance unchanged. However, this sequestration of ${}^4\mathrm{He}$ results in a decrease in the primordial ${}^7\mathrm{Li}$ abundance. Primordial abundances of ${}^7\mathrm{Li}$ consistent with observationally inferred values can be obtained for reaction rates similar to those calculated for the present-day (unbound ${}^8\mathrm{Be}$) case. Even for the largest binding energies and largest reaction rates examined here, only a small fraction of ${}^8\mathrm{Be}$ is burned into heavier elements, consistent with earlier studies. There is no change in the predicted deuterium abundance for any model we examined.

Figure 1

The primordial mass fractions of ${}^4\mathrm{He}$ (blue) and ${}^8\mathrm{Be}$ (red) along with the sum of the ${}^4\mathrm{He}$ and ${}^8\mathrm{Be}$ mass fractions (black) as a function of $B_8$, the mass difference between two ${}^4\mathrm{He}$ nuclei and a single ${}^8\mathrm{Be}$ nucleus, for $F_0=1.0\times {10}^{11}$, where $F_0$ parametrizes the ${}^4\mathrm{He}+{}^4\mathrm{He}$ rate in Eq. (12).

Figure 2

The abundance (relative to hydrogen) of ${}^7\mathrm{Li}$, as a function of $B_8$, the mass difference between two ${}^4\mathrm{He}$ nuclei and a single ${}^8\mathrm{Be}$ nucleus, for (top to bottom) $F_0=1.0\times {10}^9$ (black), $1.0\times {10}^{10}$ (magenta), $1.0\times {10}^{11}$ (red), $1.0\times {10}^{12}$ (blue), where $F_0$ parametrizes the ${}^4\mathrm{He}+{}^4\mathrm{He}$ rate in Eq. (12). The ${}^7\mathrm{Li}$ abundance is the sum of the primordial ${}^7\mathrm{Li}$ and ${}^7\mathrm{Be}$ abundances, as the latter decays into the former. Horizontal dashed lines give the range for the observationally inferred value of ${}^7\mathrm{Li}/\mathrm{H}$.