A LINEAR-PROGRAMMING APPROACH TO INHOMOGENEOUS PRIMORDIAL NUCLEOSYNTHESIS

We examine inhomogeneous primordial nucleosynthesis for arbitrary dist ributions f of the baryon-to-photon ratio eta, in the limit where neit her particle diffusion nor gravitational collapse is important. By dis cretizing f(eta) and using linear programming, we show that for a set of m constraints on the primordial element abundances, the maximum and minimum possible values of <(eta)over bar> (the final mean value of e ta) are given when f(eta) is a sum of at most m + 1 delta functions. O ur linear programming results indicate that when f is taken to be an a rbitrary function, there is no lower bound on <(eta)over bar>, while t he upper bound is essentially the homogeneous upper bound.