Investigations into Primordial Black Hole Relics and Their Potential as a Candidate for Dark Matter

Abstract

Primordial black holes (PBHs) are a theoretical type of black hole that emerged in the early universe, possibly from the collapse of enormous density fluctuations. The potential formation time of PBHs allowed for initial masses ranging from about one gram to many solar masses; additionally, if they formed in a radiation-dominated universe, the formula for PBH mass (m_PBH) will be derived as a function of the formation time (t_i) to be m_PBH ∼ 10^38(t_i/s) g. Black Holes, according to Stephen Hawking, can lose energy through thermal radiation, which leads to their evaporation. By applying this principle to PBHs, the formula for estimating the evaporation time (t_ev) will be derived and shown to satisfy the relationship t_ev ∝ m^3 PBH. The mass that has completely evaporated by today will be calculated as m_PBH = 10^15g. This evaporation process has the potential to cause the PBH to completely vanish or to decay into relics (most likely Planck mass relics), and this suggested fate results in constraints on the abundance of PBHs. In this work, it will be considered whether PBH relics can account for all of today’s dark matter, and whether there could have been a brief period when PBHs dominated the universe before decaying altogether. As a result, we obtain the maximum possible value of the PBH initial mass (equal to m_PBH = 10^10g), which explains all dark matter as PBHs, while not being ruled out by any other constraints. This leads us to the conclusion that to obtain enough relics, PBHs must evaporate before big bang nucleosynthesis, so that the known standard cosmology will not be affected by the evaporation. By estimating the maximum fraction of the universe collapse into PBH, we identify the parameter space (in the range 1g < m_i < 10^9g) where all dark matter is in PBH relics. Furthermore, we quantitatively rule out the possibility of an early matter-dominated era before the standard matter-radiation equality in which PBHs can dominate the universe.