  In Poulin and Serpico [Phys. Rev. Lett. 114, 091101 (2015)] we have recently
argued that when the energy of a photon injected in the primordial plasma falls
below the pair-production threshold, the universality of the non-thermal photon
spectrum from the standard theory of electromagnetic cascades onto a photon
background breaks down. We showed that this could reopen or widen the parameter
space for an exotic solution to the 'lithium problem'. Here we discuss another
application, namely the impact that this has on non-thermal big bang
nucleosynthesis constraints from 4He, 3He and 2H, using the parametric example
of monochromatic photon injection of different energies. Typically, we find
tighter bounds than those existing in the literature, up to more than one order
of magnitude. As a consequence of the non-universality of the spectrum, the
energy-dependence of the photodissociation cross-sections is important. We also
compare the constraints obtained with current level and future reach of cosmic
microwave background spectral distortion bounds.
