arXiv : Probing modified Hawking evaporation with gravitational waves from the primordial black hole dominated universe

Balaji, Shyam; Domènech, Guillem; Ganz, Alexander; Franciolini, Gabriele; Tränkle, Jan

doi:10.1088/1475-7516/2024/11/026

Article
Report number	arXiv:2403.14309 ; CERN-TH-2024-037
Title	Probing modified Hawking evaporation with gravitational waves from the primordial black hole dominated universe
Author(s)	Balaji, Shyam (King's Coll. London) ; Domènech, Guillem (Hannover U. ; Hannover, Max Planck Inst. Grav.) ; Franciolini, Gabriele (CERN) ; Ganz, Alexander (Hannover U.) ; Tränkle, Jan (Hannover U.)
Publication	2024-11-19
Imprint	2024-03-21
Number of pages	18
Note	18 pages+appendices, 7 figures; v2: corrected minor typos, matches published version
In:	JCAP 2411 (2024) 026
DOI	10.1088/1475-7516/2024/11/026
Subject category	hep-ph ; Particle Physics - Phenomenology ; astro-ph.CO ; Astrophysics and Astronomy ; gr-qc ; General Relativity and Cosmology
Abstract	It has been recently proposed that Hawking evaporation might slow down after a black hole has lost about half of its mass. Such an effect, called "memory burden", is parameterized as a suppression in the mass loss rate by negative powers $n$ of the black hole entropy and could considerably extend the lifetime of a black hole. We study the impact of memory burden on the Primordial Black Hole (PBH) reheating scenario. Modified PBH evaporation leads to a significantly longer PBH dominated stage. Requiring that PBHs evaporate prior enough to Big Bang Nucleosynthesis shrinks the allowed PBH mass range. Indeed, we find that for $n>2.5$ the PBH reheating scenario is not viable. The frequency of the Gravitational Waves (GWs) induced by PBH number density fluctuations is bound to be larger than about a Hz, while the amplitude of the GW spectrum is enhanced due to the longer PBH dominated phase. Interestingly, we show that, in some models, the slope of the induced GW spectrum might be sensitive to the modifications to Hawking evaporation, proving it may be possible to test the "memory burden" effect via induced GWs. Lastly, we argue that our results could also apply to general modifications of Hawking evaporation.
Copyright/License	publication: © 2024-2025 The Author(s) (License: CC BY 4.0) preprint: (License: arXiv nonexclusive-distrib 1.0)

$Evolution of the fractional energy densities $\Omega_{\rm PBH}$ (black) and $\Omega_{\rm rad}$ (red) in terms of the number of e-folds $N=\ln a$ since PBH formation at $N_{\rm f}$. The semi-classical evaporation proceeds until $N_{\rm eva}^{\rm sc}\approx 16.7$, and the memory burden effect sets in at $N_{\rm mb}\approx 16.62$. For $n=0$, memory burden is switched off, and PBH domination finishes soon after $t_{\rm mb}$ (dotted line). For larger values of $n>0$, the PBH evaporation is delayed considerably, and PBH domination lasts longer (dashed and solid lines). Parameter values for the plot are $M_{\rm f}=10 \si{\gram} ,\ \beta=10^{-3}, \ q=\frac{1}{2}$ and we consider the case mb2.$ ${\bf Left panel:} we plot the temperature at evaporation, given by Eq.~\eqref{eq:Tevamb}, as a function of $M_{\rm f}$. With the color code, we show the dependence on $n$. The red line shows the temperature at BBN, which provides the lower limit of the allowed parameter range for the temperature. The excluded parameter space is shown with a gray shaded region. We note how increasing $n$ exponentially shrinks the parameter range where PBH domination can be attained, as the evaporation is not sufficiently fast. {\bf Right panel:} we show the maximal mass $M^{\rm mb}_{\rm f,max}$, given by Eq.~\eqref{eq:Mfmax}, as a function of $n$. Note that we only considered the mb1 case as the results are qualitatively the same as in the mb2 case and differ only by a simple numerical factor. As in the left panel, the shaded region is excluded by BBN.$ $Peak frequency $f_{\rm uv}$ of the induced GW spectrum, given by Eq.~\eqref{eq:fuvmb}, as a function of $M_{\rm f}$. With the color code, we show how $f_{\rm uv}(M_{\rm f})$ depends on $n$. See how increasing the value of $n$ moves the peak to lower frequencies. The red line shows the minimum frequency allowed by BBN constraints, which, for a given $n$, gives a maximum mass $M_{\rm f}^{\rm max}$ given by Eq.~\eqref{eq:Mfmax}. While memory burden can shift the peak to lower frequencies, it can never place it below $\sim \rm Hz$. We show the excluded parameter space with a gray shaded region.$ Show more plots

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Notice créée le 2024-04-02, modifiée le 2025-04-04

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