Gravitational waves from dark domain walls

TL;DR

This paper investigates whether late-time domain walls in a dark-sector scalar field (the asymmetron/symmetron) can generate a stochastic gravitational-wave background compatible with observations like NANOGrav. It introduces a fully relativistic framework that couples scalar-field dynamics to N-body structure formation to predict the gravitational-wave spectrum, expressed through $S_h(f)$ and $\Omega_{\mathrm{gw}}(f)$ with $2\pi c^{3} S_{h}(f) = P_{\dot{h}}(k = 2\pi f/c)$ and $\Omega_{\mathrm{gw}}(f) = \frac{4\pi^{2}}{3H_0^{2}} f^{3} S_{h}(f)$. The simulations show that the GW signal from collapsing domain walls is enhanced by asymmetry in the potential ($\Delta\beta>0$), peaks near the Compton scale set by $L_{C}$, and features a low-frequency plateau influenced by large-scale structure; however, matching the amplitude observed by NANOGrav requires substantial extrapolation in $L_{C}$ and model parameters, highlighting both the potential and the challenges of late-time dark-sector GW sources. The study provides a novel toolchain (AsGRD) for exploring late-time cosmological GW production and its connections to dark-sector physics and cosmic structure formation.

Abstract

For most of cosmic history, the evolution of our Universe has been governed by the physics of a 'dark sector', consisting of dark matter and dark energy, whose properties are only understood in a schematic way. The influence of these constituents is mediated exclusively by the force of gravity, meaning that insight into their nature must be gleaned from gravitational phenomena. The advent of gravitational-wave astronomy has revolutionised the field of black hole astrophysics, and opens a new window of discovery for cosmological sources. Relevant examples include topological defects, such as domain walls or cosmic strings, which are remnants of a phase transition. Here we present the first simulations of cosmic structure formation in which the dynamics of the dark sector introduces domain walls as a source of stochastic gravitational waves in the late Universe. We study in detail how the spectrum of gravitational waves is affected by the properties of the model, and extrapolate the results to scales relevant to the recent evidence for a stochastic gravitational wave background. Our relativistic implementation of the field dynamics paves the way for optimal use of the next generation of gravitational experiments to unravel the dark sector.

Figures (4)

• Figure 1: A slice through the simulation volume at redshift $z=0.1$, showing the tensor wave intensity $\sum_{i,j}\dot{h}^{2}_{ij}/H^{2}$, where ${H}$ is the Hubble factor. Model iii@$_{\Delta \beta}$, shown on the left, has the parameters ($L_{C},z_{*},\bar{\beta},\Delta\beta/\bar{\beta})=( 1480$ kpc$, 0.1,8,10\%$). A standard cosmology without the scalar field is shown on the right. (The Supplementary Material contains animations that show the evolution of the fields and the formation of cosmic structure.)
• Figure 2: Power spectra of the time derivative of the tensor perturbation, $\dot{h}_{ij}$, plotted as dimensionless energy density per logarithmic frequency interval. The conversion from Fourier wavenumber $k$ to frequency $f$ assumes the standard dispersion relation $k = 2 \pi f / c$. Results from the simulations in the larger volume, $(742\,\mathrm{Mpc})^{3}$, are shown in the left panel and the ones for the smaller volume, $(148\,\mathrm{Mpc} )^{3}$, are shown in the right panel. The error bars indicate the 95% confidence intervals estimated from statistical fluctuations measured for each realisation within a narrow frequency band. The dotted line labelled "LSS" shows the gravitational wave contribution from the evolution of large-scale structure as predicted by second-order perturbation theory. The short blue line labelled "SMBH", inserted as a visual guide only, indicates the expected slope for an astrophysical signal produced by supermassive black hole inspirals. This signal would however appear at very different frequencies and amplitudes.
• Figure 3: The spectral index $\gamma$ inferred from the power spectra shown in figure \ref{['fig:hijprime_comparison_pk']}, with error bars indicating 95% confidence intervals. The blue bands show the 68% and 95% confidence intervals reported for the NANOGrav observations that were however taken at much higher frequencies. The dotted horizontal line labelled SMBH indicates the expected spectral index for supermassive black hole inspirals, which would also appear at much higher frequencies.
• Figure 4: Numerical tests for the power spectra of gravitational waves. The red graphs are for the parameter choice, i, presented in section \ref{['S:numerical_simulations']}, where we used a simulation volume of (148 Mpc$)^{3}$. The $\Lambda$CDM graphs in blue are using the same box volume. The graphs named 'shot noise' use 8 times as many particles. The graph 'small box' keeps the grid and particle number constant, but is using an eighth of the simulation volume, $(74$ Mpc$)^{3}$. The green graphs are for the parameter choice i@, and use a simulation volume (148 Mpc$)^3$, but with different grid resolutions of $1280^3$ and $512^3$ points, respectively. The vertical lines indicate the Nyquist scale of the (148 Mpc$)^{3}$ boxes, and the box scale of the $(74$ Mpc$)^{3}$ box.