While reading about Hawking Radiation which occurs due to quantum effects (quantum fluctuations) at the event horizon of a black hole, I was thinking whether this radiation can take place at the Big Bang singularity or at the Big Crunch singularity (if it exists). If it really happens, how does it affect the process of Big Bang (or Big Crunch)? Does the singularity disappear? Is this radiation the main cause of a Big Bang that gives birth to another universe?
The first reported observation of Hawking radiation was in the form of "Hawking points" ("circular spots of significantly raised temperature") in the Cosmic Microwave Background radiation, that were described by An, Meissner, Nurowski, and Penrose in the 2020 paper titled "Apparent evidence for Hawking Points in the CMB Sky", whose preprint's freely visible at https://arxiv.org/abs/1808.01740.pdf (which was, itself, a response to criticism of an earlier paper on the same subject), and appeared several months before Penrose's receipt of a 2020 Nobel Prize in physics. Those "points" have been considered to represent Hawking radiation from evaporation of supermassive black holes, that differ from the more common black holes which have resulted from the collapse of large rotating stars. (The supermassive variety result from collapse of a much larger region of "dust", and I believe only one has been observed to occur, in the constellation Sagitarrius, whose observation occurred several years ago [earth time].)
Although the mathematical physicist Penrose has, in collaboration with the late Stephen Hawking, written a number of "singularity theorems", I don't believe he would regard the "Hawking points" as indicative of any origin of the universe in a "Big Bang singularity", as his own cosmological model ("Conformal Cyclic Cosmology", described in his 2010 pop.-sci. book titled "Cycles of Time") is entirely compatible with a universe eternal to the past as well as to the future.
Its complete eternality is described by the Rutgers philosopher David Lindford, in a paper titled "Big Bounce or Double Bang?", whose preprint is freely visible at https://arxiv.org/abs/1808.01740.abs . (Physicists might object to analysis of a mathematical physicist's work by a philosopher, but, as Lindford was involved in an analysis of the well-publicized debate between the physicist Sean Carroll and some theologians, I think his profession was entirely appropriate for that role: Moreover, he provides a great verbal explanation of how thermodynamic entropy plays a role counterbalancing gravitational entropy, in Penrose's model.)
In CCC, all matter eventually decays into radiation. Readers as naive as I once was might confuse this decay with the mass-to-energy conversion that destroyed Hiroshima in a matter of seconds, but, as the decay described by Penrose would take place over time periods that he describes as "aeons", it would actually be more like sequential changes into particles less and less massive, and eventually into bosons (which can pass through each other). The total lack of mass adequate for the natural formation or artificial construction of any sort of time-keeping mechanism would leave the duration of the aeons undefined, although processes perhaps as simple as the absorption of solar energy by plants (in their production of sugar) would eventually restore a world perhaps much like our own, but on an almost unimaginably larger scale, as the thermodynamic equilibrium of one aeon would serve as "the" Big Bang of the next. Quantum processes would assure some differences between each aeon and the next, and, although the doesn't specify this possibility, the many bosons already present in out own aeon might perhaps remain extant as part of some unobservable "potential", like that represented by our own "virtual particles".
Penrose provided one tiny last-minute alteration to his model 26 minutes into his acceptance speech for the Nobel prize: Some few fermions would survive from each aeon into the next, I'd guess to serve as role models for its eventually colossal amounts of mass.