In this article we investigate the cumulative stochastic gravitational wave spectra as a
tool to gain insight on the creation mechanism of primordial black holes. We consider
gravitational waves from the production mechanism of primordial black holes and from the
gravitational interactions of those primordial black holes among themselves and other
astrophysical black holes. We specifically focus on asynchronous bubble nucleation during a first
order phase transition as the creation mechanism. We have used two benchmark phase transitions
through which the primordial black holes and the primary gravitational wave spectra have been
generated. We have considered binary systems and close hyperbolic interactions of primordial black
holes with other primordial and astrophysical black holes as the source of the secondary part of
the spectra. We have shown that this unique cumulative spectra have features which directly and
indirectly depend on the specifics of the production mechanism.
Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised uncertainty principle which leads to a modified Heisenberg algebra. This can alter the usual von-Neumann evolution of density matrix to a Lindblad-type equation. We show how this can give rise to a decoherence in neutrino propagation in vacuum. The decoherence effects due to the linear quadratic generalised uncertainty principle are extremely minimal and is unlikely to be detectable in the existing or upcoming experimental facilities for any of the natural sources of neutrinos. We also show that, in principle, there can be other variants of generalised uncertainty principle which predicts verifiable decoherence effects for the cosmic neutrino background.
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