Compact objects in and beyond the standard model from nonperturbative vacuum scalarization

Open Access

Compact objects in and beyond the standard model from nonperturbative vacuum scalarization

Loris Del Grosso, Paolo Pani, and Alfredo Urbano

Phys. Rev. D 109, 095006 – Published 6 May 2024

Abstract

We consider a theory in which a real scalar field is Yukawa coupled to a fermion and has a potential with two nondegenerate vacua. If the coupling is sufficiently strong, a collection of $N$ fermions deforms the true vacuum state, creating energetically favored false-vacuum pockets in which fermions are trapped. We embed this model within general relativity and prove that it admits self-gravitating compact objects where the scalar field acquires a nontrivial profile due to nonperturbative effects. We discuss some applications of this general mechanism: (i) “neutron soliton stars” in low-energy effective QCD, which naturally happen to have masses around $2 M_{⊙}$ and radii around 10 km even without neutron interactions; (ii) “Higgs false-vacuum pockets” in and beyond the standard model; (iii) “dark soliton stars” in models with a dark sector. In the latter two examples, we find compelling solutions naturally describing centimeter-size compact objects with masses around $10^{- 6} M_{⊙}$ , intriguingly in a range compatible with the Optical Gravitational Lensing $Experiment (OGLE) + Hyper$ Suprime-Cam (HSC) microlensing anomaly. In addition to these interesting examples, the mechanism of nonperturbative vacuum scalarization may play a role in various contexts in and beyond the standard model, providing a support mechanism for new compact objects that can form in the early Universe, can collapse into primordial black holes through accretion past their maximum mass, and serve as dark matter candidates.

Received 20 January 2024
Accepted 26 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.095006

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)

Classical solutions in field theory Cosmology Dark matter General relativity

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Loris Del Grosso , Paolo Pani , and Alfredo Urbano

Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy and INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy

Article Text

Click to Expand

References

Click to Expand

Issue

Vol. 109, Iss. 9 — 1 May 2024

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Pictorial illustration of the nonperturbative vacuum scalarization Sketch of the mechanism, showing the energy $E$ of different configurations as a function of $η$ , a fundamental parameter defined in Eq. (16). The bigger $η$ the more the theory becomes strongly coupled. The orange balls represent massive fermions, whereas the yellow balls represent the false vacuum pockets of the scalar field in which the fermions are massless (and therefore depicted by smaller orange balls). (a) Standard ground state of the system. (b), (c) Whenever $η ≳ 1$ , it is energetically convenient for the system to trap a fraction of fermions in false vacuum pockets. For $η ≲ 1$ , equilibrium configurations describing bound false vacuum pockets do not exist.
Reuse & Permissions
Figure 2
Effective scalar potential [see Eq. (19)] normalized with respect to $U_{0} = λ v^{4} / 16$ as a function of $h / v$ for various values of $η$ in the Newtonian regime. In this regime, the zeros of the Fermi momentum are $h / v = \pm {\tilde{ω}}_{F}$ (for $| h | / v > {\tilde{ω}}_{F}$ the fermions are removed from the theory). We fixed a representative value ${\tilde{ω}}_{F} = 0.5$ . We notice that when $η ≳ 1$ the effective potential develops a local minimum in $h = 0$ . The shape of the potential is qualitatively the same also in the fully relativistic regime.
Reuse & Permissions
Figure 3
Radial profiles of scalar field $h$ , normalized with respect to $v$ , metric functions $u$ , $v$ (left) and fermion pressure (right) for a typical configuration ( $Λ = 0.075$ , $η = 4$ ). Continuous lines represent numerical data, whereas dashed lines reconstruct the asymptotic behavior of the solution by fitting with the Schwarzschild spacetime. The mass and radius of this configuration are $μ M / m_{p}^{2} \approx 4.08$ and $μ R \approx 14.96$ , the compactness is $C \approx 0.27$ , while the solution parameters are ${\tilde{P}}_{c} = 8.8 \times 10^{- 3}$ and $\log_{10} ε = - 19.00$ . The binding energy is $μ E_{B} / m_{p}^{2} \approx - 5.10$ .
Reuse & Permissions
Figure 4
Mass-radius (left) and compactness-mass (right) diagrams for various values of $η$ . We fixed $Λ = 0.075$ . Varying $Λ$ does not change the results qualitatively. There exists a turning point in the $M - R$ diagrams at low masses, which cannot be seen from the figure, that proceeds toward the Newtonian limit of small $M$ and large $R$ , similar to what was already shown in [22].
Reuse & Permissions
Figure 5
Left: rescaled mass-radius diagrams for various $Λ$ . We fix $η = 4$ . Varying $η$ does not produce appreciable changes as long as we stay in the confining regime $η ≳ 1$ . As expected, there is an approximate scaling law as $\sim 1 / Λ$ , which becomes more and more accurate as $Λ \to 0$ . Right: mass as a function of ${\tilde{ω}}_{F}$ for various values of $η$ . We fixed $Λ = 0.075$ . Varying $Λ$ does not change the results qualitatively. Notice the existence of a minimum value for ${\tilde{ω}}_{F}$ at any given $η$ .
Reuse & Permissions
Figure 6
The initial displacement (left) and binding energy (right) for various values of $η$ . We fixed $Λ = 0.075$ . Varying $Λ$ does not change the results qualitatively. As expected, the bigger $η$ , the lower the binding energy. The configurations corresponding to the critical ones are highlighted with a violet marker.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology