  Using the upper bound on the effective number of light neutrino species
during primordial nucleosynthesis and the cosmological pion-pole mechanism
$\gamma\gamma\rightarrow \pi^0\rightarrow \gamma X$, we obtain an upper limit
on the branching ratio for the decay BR$(\pi^0\rightarrow \gamma X)<3\times
10^{-13}$, where $X$ is any long-lived weakly interacting neutral vector
particle with mass smaller than the neutral pion mass.
