  Big-bang nucleosynthesis (BBN) probes the cosmic mass-energy density at
temperatures $\sim 10$ MeV to $\sim 100$ keV. Here, we consider the effect of a
cosmic matter-like species that is non-relativistic and pressureless during
BBN. Such a component must decay; doing so during BBN can alter the
baryon-to-photon ratio, $\eta$, and the effective number of neutrino species.
We use light element abundances and the cosmic microwave background (CMB)
constraints on $\eta$ and $N_\nu$ to place constraints on such a matter
component. We find that electromagnetic decays heat the photons relative to
neutrinos, and thus dilute the effective number of relativistic species to
$N_{\rm eff} < 3$ for the case of three Standard Model neutrino species.
Intriguingly, likelihood results based on {\em Planck} CMB data alone find
$N_{\nu} = 2.800 \pm 0.294$, and when combined with standard BBN and the
observations of D and \he4 give $N_{\nu} = 2.898 \pm 0.141$. While both results
are consistent with the Standard Model, we find that a nonzero abundance of
electromagnetically decaying matter gives a better fit to these results. Our
best-fit results are for a matter species that decays entirely
electromagnetically with a lifetime $\tau_X = 0.89 \ \rm sec$ and pre-decay
density that is a fraction $\xi = (\rho_X/\rho_{\rm rad})|_{10 \ \rm MeV} =
0.0026$ of the radiation energy density at 10 MeV; similarly good fits are
found over a range where $\xi \tau_X^{1/2}$ is constant. On the other hand,
decaying matter often spoils the BBN+CMB concordance, and we present limits in
the $(\tau_X,\xi)$ plane for both electromagnetic and invisible decays. For
dark (invisible) decays, standard BBN (i.e. $\xi=0$) supplies the best fit. We
end with a brief discussion of the impact of future measurements including
CMB-S4.
