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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 thefraction 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 importantargument that baryons can contribute at most 10\% of critical density and thuscannot close the Universe. Nonstandard scenarios involving decayingparticles,$^1$ inhomogeneities in the baryon density,$^2$ and even more exoticideas$^3$ put forth to evade this bound have been largely unsuccessful.$^4$ Wesuggest 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 productsinclude electron neutrinos, the bound to the baryon mass density can beloosened by a about factor of $10$. The key is the decay-generated electronantineutrinos: around the time of nucleosynthesis they are captured by protonsto produce neutrons, thereby changing the outcome of nucleosynthesis.Experiments at $e^\pm$ colliders should soon be sensitive to a tau-neutrinomass in the required range.Comment: 10p, FERMILAB Pub-94/059A, Figs available on reques

Relaxing the big-bang bound to the baryon density