Cosmological Implications of the Slingshot Effect: Gravitational Waves, Primordial Black Holes and Dark Matter

Abstract

In this paper, we explore the implications of the so-called slingshot effect. It represents a rather general phenomenon occurring when a localized source, such as a monopole, quark, or a $D$-brane, crosses a domain wall separating the confined (Higgsed) and unconfined (Coulomb) phases of the crossing source. The crossover is accompanied by a stretched ``string'' of proper co-dimensionality that confines the source to the domain wall. The effect takes place for different setups, such as phase transitions leading to confinement, both electric and magnetic, as well as in string theoretic inflation with $D$-branes. We discuss the role of the phenomenon in sourcing gravitational waves and dark matter in the form of Kaluza-Klein gravitons. We also show that the slingshot effect can lead to the formation of primordial black holes in observationally interesting mass ranges for dark matter and high-energy cosmic rays.

Figures (4)

• Figure 1: The magnetic energy density in the $y=0$ plane at time $t=115\, m^{-1}_{v_\phi}$ in units $m_{v_\phi}^4/g^2$. The black lines illustrate the contour $\abs{\psi}=0.5\, v_\psi$. Here, we chose the following parameters: $m_{h_\phi}=\sqrt{2\lambda_\phi} v_\phi=m_{v_\phi}$, $m_{v_\psi}=g v_\psi /\sqrt{2}=0.15\, m_{v_\phi}$, $m_{h_\psi}=2\sqrt{\lambda_\psi}v_\psi^2=0.6\, m_{v_\phi}$, $\beta=0.01\, m_{v_\phi}$. This figure appeared first in Bachmaier:2023wzz.
• Figure 2: The upper two plots show one time frame of the magnetic energy density in the $y=0$ plane for the monopole and antimonopole with no relative twist (left) and with maximal twist (right) entering the Higgsed region. The black lines illustrate the contour $\abs{\psi}=0.16\, m_{v_\phi}$. The initial separation distance between the two magnetic monopoles was $d=34\, m_{v_\phi}^{-1}$ for both cases. The lower two plots show one time frame of two slingshots with initial separation $d=60\, m_{v_\phi}^{-1}$ with no relative twist (left) and with maximal twist (right). The red density plot shows the magnetic energy for values bigger than $5.0 \cdot 10^{-6}\, m_{v_\phi}^4/g^2$(left) and $2.0 \cdot 10^{-5}\,m_{v_\phi}^4/g^2$(right). The blue contour plot shows the domain wall profile value $\abs{\psi}=0.2\, m_{v_{\phi}}$. Here, we chose the following parameters: $m_{h_\phi}=m_{v_\phi}$, $m_{v_\psi}=0.2\, m_{v_\phi}$, $m_{h_\psi}=0.6\, m_{v_\phi}$, $\beta=0.01\, m_{v_\phi}$.
• Figure 3: The time evolution of a growing bubble that is colliding with magnetic monopoles, leading to many slingshot events. The blue density plot shows $\abs{\phi}$ and illustrates the position of the monopoles. The orange density plot corresponds to $\abs{\psi}$ and displays the domain walls and strings. The figure shows a box of size $(170\, m_{v_\phi}^{-1})^3$. The full simulation was performed in a lattice of size $180\, m_{v_\phi}^{-1}\cross 180\, m_{v_\phi}^{-1} \cross 360\, m_{v_\phi}^{-1}$ and lattice spacing $1.0\, m_{v_\phi}^{-1}$. Here: $m_{h_\phi}=m_{v_\phi}$, $m_{v_\psi}=0.15\, m_{v_\phi}$, $m_{h_\psi}=0.6\, m_{v_\phi}$, $\beta=0.2\, m_{v_\phi}$.
• Figure 4: The red area indicates the region in which the field-theoretic slingshot (monopole slingshot) can potentially generate a gravitational radiation signal. The solid red line corresponds to the bound arising from monopole domination for a monopole mass of $M \sim 10^{16}\,\mathrm{GeV}$ (see equation \ref{['eq:monopole-domination']}). For parameters below the dashed red line, the Coulomb interaction is relevant on slingshot timescales (see equation \ref{['eq:condition-collapse-faster-than-Coulomb-attraction']}). The blue region shows the regime in which the wrapped $D$-brane slingshot can produce a gravitational radiation signal. The blue line illustrates the bound imposed by the requirement that the slingshots do not dominate the energy budget of the Universe (see equation \ref{['eq:maximal-slingshot-number-Dbrane-slingshot']}). The sensitivity curves for LISA LISA:2017pwj, aLIGO aLIGO:2020wna, and the Einstein Telescope Sathyaprakash:2012jk were obtained using the open-access code provided in Mingarelli:2019mvk. A Hubble constant of $68\,\mathrm{km/s/Mpc}$ was adopted.