Cosmological Bound on the Decay $\pi^0\rightarrow\gamma X$

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.