  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
$100\kms\Mpc^{-1}$). 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
$20\MeV-30\MeV$ 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.
