Ascertain the value of the memory burden suppression parameter k

Ascertain the physical value of the parameter k that quantifies the suppression of the evaporation rate due to the memory burden effect in primordial black holes, where the emission rate beyond half-decay is reduced by a factor proportional to S(qM0)^{-k} relative to the semiclassical rate; determine k from first-principles theory or observational inference to enable definitive constraints on the primordial black hole dark matter fraction.

Background

The analysis introduces a suppression exponent k controlling the strength of the memory burden effect, implemented as a power of the black hole entropy. Constraints throughout the paper are presented as functions of k because its value is not established.

Pinning down k is pivotal for assessing whether light primordial black holes can constitute dark matter and for specifying the size of the newly opened mass window under the memory burden hypothesis.