Connecting the Higgs potential and primordial black holes

Open Access

Connecting the Higgs potential and primordial black holes

De-Chang Dai, Ruth Gregory, and Dejan Stojkovic

Phys. Rev. D 101, 125012 – Published 15 June 2020

Abstract

It was recently demonstrated that small black holes can act as seeds for nucleating decay of the metastable Higgs vacuum, dramatically increasing the tunneling probability. Any primordial black hole lighter than $4.5 \times 10^{14} g$ at formation would have evaporated by now, and in the absence of new physics beyond the standard model, would therefore have entered the mass range in which seeded decay occurs, however, such true vacuum bubbles must percolate in order to completely destroy the false vacuum; this depends on the bubble number density and the rate of expansion of the universe. Here, we compute the fraction of the universe that has decayed to the true vacuum as a function of the formation temperature (or equivalently, mass) of the primordial black holes, and the spectral index of the fluctuations responsible for their formation. This allows us to constrain the mass spectrum of primordial black holes given a particular Higgs potential and conversely, should we discover primordial black holes of definite mass, we can constrain the Higgs potential parameters.

Received 6 September 2019
Accepted 3 June 2020

DOI:https://doi.org/10.1103/PhysRevD.101.125012

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cosmology Quantum fields in curved spacetime Spontaneous symmetry breaking Vacuum stability

Particles & Fields

Authors & Affiliations

De-Chang Dai ^1,2, Ruth Gregory ^3,4, and Dejan Stojkovic⁵

¹Center for Gravity and Cosmology, School of Physics Science and Technology, Yangzhou University, 180 Siwangting Road, Yangzhou City, Jiangsu Province 225002, People’s Republic of China
²CERCA/Department of Physics/ISO, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA
³Centre for Particle Theory, Durham University, South Road, Durham DH1 3LE, United Kingdom
⁴Perimeter Institute, 31 Caroline Street, Waterloo, Ontario N2L 2Y5, Canada
⁵HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, New York 14260-1500, USA

Article Text

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Issue

Vol. 101, Iss. 12 — 15 June 2020

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Images

Figure 1
The branching ratio between the tunneling and evaporation rate as a function of the seed black hole mass, $M_{+}$ , for some sample choices of the potential parameters. The unit branching ratio, $Γ_{D} / Γ_{H} = 1$ , is labeled by the dotted line. We set $b = 1.5 \times 10^{- 5}$ , $c = 0$ . $M_{+}$ is given in units of $M_{p}$ .
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Figure 2
A plot of the line $\frac{Γ_{D}}{Γ_{H}} = 1$ in $(b, λ_{*})$ parameter space for the values $c = 0$ , $6.3 \times 10^{- 8}$ as labeled. Above the curve, the branching ratio $\frac{Γ_{D}}{Γ_{H}}$ is always less than one for any value of the seed black hole mass. Below the curve, there is always a range of the black hole masses for which the branching ratio $\frac{Γ_{D}}{Γ_{H}}$ is greater than one. The dependence on $c$ is minimal.
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Figure 3
The present number density of the true vacuum bubbles, plotted as a function of the temperature at which the primordial black holes that seed nucleation are formed. The number density is shown for two values of the spectral density index, $n$ , of the perturbations responsible for the primordial black hole creation.
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Figure 4
This plot shows the temperature of the universe at the time of the primordial black hole formation, $T_{F}$ , as a function of the spectral index, $n$ for several values of the black hole masses that can trigger the vacuum decay. The lines represent the $P = 1$ value for the portion of the universe which already transitioned to the new vacuum at present time. Above these lines, we have $P > 1$ and the whole universe today would be destroyed. Below these lines we have $P < 1$ , and the universe is safe. A black hole of the initial mass $M_{i}$ (determined by the formation temperature $T_{F}$ ) evaporates and triggers the vacuum decay at some lower value $M_{dec}$ . If $M_{i} > M_{dec}$ , the onset of the phase transition is delayed by the time needed for a black hole to enter the window where it can trigger the vacuum decay with $\frac{Γ_{D}}{Γ_{H}} > 1$ . The solid line corresponds to the black hole masses $M_{dec} ≪ 5 \times 10^{14} g$ , i.e., $M_{dec} \approx 0$ . The dashed, dot, dashed dot, and dashed dot dot lines correspond to $M_{dec}$ values of $5 \times 10^{14} g$ , $10^{15} g$ , $10^{16} g$ , $10^{17} g$ . The short dashed line corresponds to $M_{i} < M_{dec}$ , where such black holes trigger the vacuum decay immediately upon formation.
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Figure 5
This plot shows the primordial black hole masses (in grams) at the time of their formation, $M_{i}$ , as a function of the spectral index, $n$ . The lines represent the $P = 1$ value for the portion of the universe which already transitioned to the new vacuum at present time. Below this line we have $P > 1$ and the whole universe today would be destroyed. Above this line, we have $P < 1$ , and the universe is safe. The solid line corresponds to the black hole masses $M_{dec} ≪ 5 \times 10^{14} g$ , i.e., $M_{dec} \approx 0$ . The dashed, dot, dashed dot, and dashed dot dot lines correspond to $M_{dec}$ values of $5 \times 10^{14} g$ , $10^{15} g$ , $10^{16} g$ , $10^{17} g$ . The short dashed line corresponds to $M_{i} < M_{dec}$ , where such black holes trigger the vacuum decay immediately upon formation.
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Figure 6
This plot shows the primordial black hole masses (in grams) at the time of their formation, $M_{i}$ , as a function of the spectral index, $n$ . The solid lines represent the $P = 1$ value for the portion of the universe which already transitioned to the new vacuum at present time. Below this line we have $P > 1$ and the whole universe today would be destroyed. Above this line, we have $P < 1$ , and the universe is safe. The dashed, dot, dashed dot and dashed dot dot lines represent the values $P = 10^{- 1}$ , $P = 10^{- 2}$ , $P = 10^{- 3}$ and $P = 10^{- 4}$ respectively, where the phase transition has not completed yet, but there are bubbles of true vacuum present in the universe.
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