  We derive constraints on the injection of free-streaming dark radiation after
big bang nucleosynthesis (BBN) by considering the decay of a massive hidden
sector particle into dark radiation. Such a scenario has the potential to
alleviate the Hubble tension by introducing a new energy component to the
evolution of the early universe. We employ observations of the cosmic microwave
background (CMB) from $\textit{Planck}$ 2018 and the South Pole Telescope
(SPT-3G), measurements of the primordial deuterium abundance, Pantheon+ Type Ia
supernovae data, and baryon acoustic oscillation (BAO) measurements from BOSS
DR12 to constrain these decay scenarios. Pre-recombination decays are primarily
restricted by observations of the CMB via their impact on the effective number
of relativistic species. On the other hand, long-lived decay scenarios in which
the massive particle lifetime extends past recombination tend to decrease the
late-time matter density inferred from the CMB and are thus subject to
constraints from Pantheon+ and BAO. We find that, when marginalizing over
lifetimes of $\tau_Y = [10^{-12.08}, 10^{-1.49}]$ Gyr, the decaying particle is
limited at $2\sigma$ to only contribute a maximum of $3\%$ of the energy
density of the universe. With limits on these decays being so stringent,
neither short-lived nor long-lived scenarios are successful at substantially
mitigating the Hubble tension.
