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A linear programming approach to inhomogeneous primordial nucleosynthesis

We examine inhomogeneous primordial nucleosynthesis for {\it arbitrary} distributions $f$ of the baryon-to-photon ratio $η$, in the limit where neither particle diffusion nor gravitational collapse is important. By discretizing $f(η)$ 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 $\bar η$ (the final mean value of $η$) are given when $f(η)$ is a sum of at most $m+1$ delta functions. Our linear programming results indicate that when $f$ is taken to be an arbitrary function, there is no lower bound on $\bar η$, while the upper bound is essentially the homogeneous upper bound.