We derive new CMB anisotropy power spectrum and BBN constraints for evaporating primordial black holes with mass between 1011 g and 1016 g by explicitly solving the electromagnetic particle cascades of emitted particles and the deposition of this emitted energy to the background baryon-photon plasma. We show that the CMB anisotropies can provide stronger constraints compared to BBN and CMB spectral distortions on black holes with masses as small as MBH=1.1× 1013 g, a slightly smaller mass than what has been considered in literature until now. We also show that, with more up-to-date data on abundances of deuterium and helium-3, BBN constraints are strengthened significantly. The abundance of these primordial black holes constrains the epoch of inflation 0∼ 4 e-folds after the epoch constrained by the CMB observations.

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 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 10000 (lifetime τ X 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.

Current constraints on energy injection in the form of energetic particles before the epoch of recombination using CMB spectral distortions assume that all energy goes into y and µ-type distortions. We revisit these constraints with exact calculations of the spectral distortions by evolving the electromagnetic cascades. The actual spectral distortion differs in shape and amplitude from the y-type distortion and depends on the energy and nature of injected particles. The constraints on the energy injection processes such as dark matter decay can be relaxed by as much as a factor of 5.

Spectral distortions of the cosmic microwave background (CMB) provide a unique tool for learning about the early phases of cosmic history, reaching deep into the primordial Universe. At redshifts z ≲ 106, thermalization processes become inefficient and existing limits from COBE/FIRAS imply that no more than Δρ/ρ ≲ 6 × 10−5 ($95\%$ c.l.) of energy could have been injected into the CMB. However, at higher redshifts, when thermalization is efficient, the constraint weakens and Δρ/ρ ≃ 0.01 − 0.1 could in principle have occurred. Existing computations for the evolution of distortions commonly assume Δρ/ρ ≪ 1 and thus become inaccurate in this case. Similarly, relativistic temperature corrections become relevant for large energy release, but have previously not been modeled as carefully. Here we study the evolution of distortions and the thermalization process after single large energy release at z ≳ 105. We show that for large distortions the thermalization efficiency is significantly reduced and that the distortion visibility is sizeable to much earlier times. This tightens spectral distortions constraints on low-mass primordial black holes with masses MPBH ≲ 2 × 1011 g. Similarly, distortion limits on the amplitude of the small-scale curvature power spectrum at wavenumbers k ≳ 104 Mpc−1 and short-lived decaying particles with lifetimes tX ≲ 107 s are tightened, however, these still require a more detailed time-dependent treatment. We also briefly discuss the constraints from measurements of the effective number of relativistic degrees of freedom and light element abundances and how these complement spectral distortion limits.