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Interaction of domain walls with scalar particles in the early Universe

D. P. Filippov, A. A. Kirillov

TL;DR

The paper addresses how domain walls formed in the early Universe interact with a bath of scalar dark matter and how this interaction can delay or prevent primordial black hole formation. It develops a scalar-field–domain-wall framework, deriving the scalar reflection coefficient $R$ and identifying a critical temperature $T_c$ below which walls become opaque and trap particles inside. The wall dynamics are governed by a coupled set of equations for the wall radius, velocity, internal/external temperatures, and number densities, revealing that internal gas pressure can counteract surface tension and Hubble drag, leading to delayed PBH formation for certain formation times. The work provides mass- and formation-time–dependent constraints on model parameters $(f,\Lambda)$ and discusses potential astrophysical consequences such as delayed PBH formation, DM protohalos around PBHs, and possible EM or GW signals, highlighting the broader implications for early-Universe cosmology and dark matter interactions.

Abstract

The formation of solitons (such as closed domain walls) in the super-Early Universe is predicted in a number of theories of the formation of primordial black holes. However, the interaction of particles of the surrounding medium with the solitons should affect their dynamics. In the paper, we consider the interaction between domain walls and scalar particles which can play a role of dark matter. It is shown that when the temperature of the scalar particle gas, caused by the expansion of the Universe, decreases below a certain threshold value, the wall abruptly becomes opaque and locks particles inside itself. We discuss the dynamics of a single domain wall taking into account pressure of scalar particles locked inside a closed wall. It is shown, this effect leads to a time delay of domain wall collapse and the deferred formation of primordial black holes.

Interaction of domain walls with scalar particles in the early Universe

TL;DR

The paper addresses how domain walls formed in the early Universe interact with a bath of scalar dark matter and how this interaction can delay or prevent primordial black hole formation. It develops a scalar-field–domain-wall framework, deriving the scalar reflection coefficient and identifying a critical temperature below which walls become opaque and trap particles inside. The wall dynamics are governed by a coupled set of equations for the wall radius, velocity, internal/external temperatures, and number densities, revealing that internal gas pressure can counteract surface tension and Hubble drag, leading to delayed PBH formation for certain formation times. The work provides mass- and formation-time–dependent constraints on model parameters and discusses potential astrophysical consequences such as delayed PBH formation, DM protohalos around PBHs, and possible EM or GW signals, highlighting the broader implications for early-Universe cosmology and dark matter interactions.

Abstract

The formation of solitons (such as closed domain walls) in the super-Early Universe is predicted in a number of theories of the formation of primordial black holes. However, the interaction of particles of the surrounding medium with the solitons should affect their dynamics. In the paper, we consider the interaction between domain walls and scalar particles which can play a role of dark matter. It is shown that when the temperature of the scalar particle gas, caused by the expansion of the Universe, decreases below a certain threshold value, the wall abruptly becomes opaque and locks particles inside itself. We discuss the dynamics of a single domain wall taking into account pressure of scalar particles locked inside a closed wall. It is shown, this effect leads to a time delay of domain wall collapse and the deferred formation of primordial black holes.
Paper Structure (4 sections, 27 equations, 4 figures)

This paper contains 4 sections, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Reflection coefficient
  3. Evolution of the domain wall
  4. Results and discussion

Figures (4)

  • Figure 1: Reflection coefficient $R$ as a function of temperature $T$. $T_6 = 10^6$ GeV.
  • Figure 2: Solid lines represent the cases when the domain walls (formed at $N$-th e-fold) interact with the scalar particles, while transparent lines show the cases without interactions. The dashed horizontal lines are the gravitational radii of DWs for each case. The normalization constants are $r_i = 10^6$ cm and $t_i=10^{-5}$ s.
  • Figure 3: The parameter space of the field model \ref{['eq:wall']} vs e-fold number $N$ on which a domain wall should begin to form in order to produce PBH (green area). The forbidden region is marked in red ($M > M_\text{max}$, see Eq. \ref{['eq:Mmax']}). A domain wall formed with the parameters marked in the blue area could not produce PBH because $r_g < d$. For the purple area, $r_i < d$.
  • Figure 4: The result of the numerical solution of the system of Eqs. \ref{['eq:motion']}, \ref{['eq:inside']} and \ref{['eq:outside']} for the case when DW was formed at $N=22$. In contrast to the case presented in Fig. \ref{['fig.2']}, the parameters are changed so that DW is able to collapse into a black hole ($f = 3\times10^{9}$ GeV and $\Lambda = 3$ GeV).