# Density Induced Vacuum Instability

### Submission summary

 As Contributors: Konstantin Springmann · Andreas Weiler Preprint link: scipost_202111_00062v2 Date submitted: 2022-06-10 16:26 Submitted by: Springmann, Konstantin Submitted to: SciPost Physics Academic field: Physics Specialties: Gravitation, Cosmology and Astroparticle Physics High-Energy Physics - Phenomenology

### Abstract

We consider matter density effects in theories with a false ground state. Large and dense systems, such as stars, can destabilize a metastable minimum and allow for the formation of bubbles of the true minimum. We derive the conditions under which these bubbles form, as well as the conditions under which they either remain confined to the dense region or escape to infinity. The latter case leads to a phase transition in the universe at star formation. We explore the phenomenological consequences of such seeded phase transitions.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission scipost_202111_00062v3 on 25 November 2022

Resubmission scipost_202111_00062v2 on 10 June 2022
Submission scipost_202111_00062v1 on 29 November 2021

## Reports on this Submission

### Report

I am satisfied with the changes made by the authors. In my opinion, the paper can be published in SciPost Physics.

### Attachment

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Report

The paper explores the consequences of finite density effects for vacuum instability. It is argued that high-density systems such as stars might destabilize a metastable minimum (basically by removing the potential barrier) and allow for the formations of bubbles of the true minimum which, under some conditions, might escape the dense system and extend to infinity. The authors mainly focus on the case where the scalar field can classically move to the true minimum of the potential, although they also briefly analyze the case where the barrier has not completely disappeared and the transition happens via quantum tunnelling. These considerations apply to a general class of scalar potentials, featuring a density dependent potential barrier. Paradigmatic examples are relaxion potentials, which are set by the QCD quark condensate or by the Higgs VEV, both acquiring a non-trivial dependence from finite density. The phenomenological consequences of these density-induced vacuum transitions are intriguing: late phase transitions at stars formations which change the vacuum energy and might leave an imprint in cosmological observations.

The paper is well structured and clearly written. Moreover, I find the results original and relevant, and therefore I recommend that the present study is published in SciPost Physics, after the following minor points are addressed:

1. It would be good to clarify better the role of density effects on the rolling term in the potential in eq. 1. Is the assumption of neglecting the density dependence in Lambda_R motivated in some explicit realizations ?

2. sect. 4.4: it seems to me that the author never consider the case in which the minimum is deep, but not in the thin-wall regime. Is this because the authors have in mind a specific class of models?

3. Related to the previous question, are there potential consequences of finite-density effects on the SM vacuum decay rate?

• validity: high
• significance: high
• originality: top
• clarity: high
• formatting: excellent
• grammar: excellent

### Author:  Konstantin Springmann  on 2022-09-22  [id 2839]

(in reply to Report 1 on 2022-07-10)

We thank the referee for the insightful comments and interesting questions on our manuscript. Below we address in detail each of the points raised.

1) Density dependent rolling scale

In this work, neglecting the density dependence of the rolling term is motivated by the explicit realization of relaxion models. In these models, although the rolling term is also slightly density dependent, the dominant effect due to SM matter density is the change in the height of the barriers. However, we agree with the referee that a density-dependent rolling scale is indeed interesting. In fact, in a subsequent work Balkin:2021, we investigated a technicolored relaxion where the rolling scale is actually increased due to a background electro-magnetic field, and similar conclusions as for a matter density dependent backreaction scales hold.

2) Barrier height vs. bubble thickness

The case of a deep minimum following our potential in Eq. 1 is by construction the case where the barrier height is much larger than the energy difference of the two vacua. This means by definition that we are in the thin wall case. In that sense, having a deep minimum is equivalent to having a thin-wall bubble. Of course, one could have parameters such that the potential is neither deep nor shallow, in which case the thin wall approximation would not hold.

3) Stability of the SM vacuum

The destabilization of the Higgs potential typically occurs at high scales, i.e. $\Lambda_{UV}\sim10^{12} \,\text{GeV}$, see Degrassi:2012ry. The linear coupling of the Higgs to SM density effectively adds a term to the Higgs potential of the order of $\Delta V \sim\rho H$. However, this linear term cannot compete with a quartic in the potential $\lambda H^4$ at $\left\langle H\right\rangle\sim 10^{12} \text{GeV}$ even at the highest known densities in compact SM objects $\rho \lesssim \text{GeV}^3$ .

### Anonymous on 2022-11-25  [id 3073]

(in reply to Konstantin Springmann on 2022-09-22 [id 2839])

We thank the referee again for the insightful comments and interesting questions.

We now added minor changes, as suggested.

1) Concerning the density dependence of the rolling scale, we would like to point the reader to the paragraph below Eq. 5, where we give explicit models where the dominant density dependence is in the backreaction scale. Below Eq. 6 we added a sentence where we refer to a model where the dominant effect is due to a background dependent rolling scale. Note that there the role of the background is played by electromagnetic fields.

2) We added a sentence in section 4.4 which clarifies that with our potential the thin wall approximation always holds for deep minima.

3) We added a sentence above Eq. 16 which points out the relevant scales at which our effect is important. Since the scales required to destabilize the SM vacuum are much higher, it can never be destabilized by the mechanism described.