CMB anisotropy and BBN constraints on pre-recombination decay of dark matter to visible particles

Injection of high energy electromagnetic particles around the recombination epoch can modify the standard recombination history and therefore the CMB anisotropy power spectrum. Previous studies have put strong constraints on the amount of electromagnetic energy injection around the recombination era (redshifts $z\lesssim 4500$). However, energy injected in the form of energetic ($>$ keV) visible standard model particles is not deposited instantaneously. The considerable delay between the time of energy injection and the time when all energy is deposited to background baryonic gas and CMB photons, together with the extraordinary precision with which the CMB anisotropies have been measured, means that CMB anisotropies are sensitive to energy that was injected much before the epoch of recombination. We show that the CMB anisotropy power spectrum is sensitive to energy injection even at $z = 10000$, giving stronger constraints compared to big bang nucleosynthesis and CMB spectral distortions. We derive, using Planck CMB data, the constraints on long-lived unstable particles decaying at redshifts $z\lesssim 10000$ (lifetime $\tau_X\gtrsim 10^{11}$s) by explicitly evolving the electromagnetic cascades in the expanding Universe, thus extending previous constraints to lower particle lifetimes. We also revisit the BBN constraints and show that the delayed injection of energy is important for BBN constraints. We find that the constraints can be weaker by a factor of few to almost an order of magnitude, depending on the energy, when we relax the quasi-static or on-the-spot assumptions.