Relaxing the Big-bang Bound to the Baryon Density

In the standard picture of big-bang nucleosynthesis the yields of D, ${}^3$He, ${}^4$He, and ${}^7$Li only agree with their inferred primordial abundances if the fraction of critical density contributed by baryons is between $0.01h^{-2}$ and $0.02h^{-2}$ ($h$ is the present value of the Hubble constant in units of $100\text{kms}{\text{Mpc}}^{-1}$). This is the basis of the very convincing and important argument that baryons can contribute at most 10% of critical density and thus cannot close the Universe. Nonstandard scenarios involving decaying particles,${}^1$ inhomogeneities in the baryon density,${}^2$ and even more exotic ideas${}^3$ put forth to evade this bound have been largely unsuccessful.${}^4$ We suggest a new way of relaxing the bound: If the tau neutrino has a mass of $20\text{MeV}-30\text{MeV}$ and lifetime of $200\sec -1000\sec$, and its decay products include electron neutrinos, the bound to the baryon mass density can be loosened by a about factor of $10$. The key is the decay-generated electron antineutrinos: around the time of nucleosynthesis they are captured by protons to produce neutrons, thereby changing the outcome of nucleosynthesis. Experiments at $e^{\pm }$ colliders should soon be sensitive to a tau-neutrino mass in the required range.