Irreducible cosmological backgrounds of a real scalar with a broken symmetry

TL;DR

This work investigates a minimal SM extension by a real singlet scalar $S$ with an approximate $\mathbb{Z}_2$ symmetry, leading to a long-lived domain-wall network whose evolution impacts gravitational waves, dark matter, and an unavoidable freeze-in background. The authors map three benchmark regimes: (i) PTA-scale gravitational waves from domain-wall annihilation with $m_s$ near the PeV scale; (ii) dark matter from domain-wall annihilation for $m_s \gtrsim 10\,\mathrm{GeV}$ requiring extremely small Higgs mixing; and (iii) an IR-dominated freeze-in production of $s$ that yields cosmological and astrophysical constraints independent of GW signals. They derive analytic expressions for the mass spectrum, decay channels, and thermal corrections, and examine thermal vs non-thermal domain-wall production, annihilation dynamics, and the resulting observational implications including PTA fits, DM abundance, and BBN/CMB/X-ray bounds. The paper highlights the interplay between domain-wall physics, gravitational waves, and dark matter in a simple portal framework, illustrating how irreducible freeze-in effects can provide robust, testable signatures even when GW or DM signals are suppressed. The findings emphasize that upcoming GW detectors and cosmological surveys can probe this minimal yet rich cosmological scenario.

Abstract

We explore the irreducible cosmological implications of a singlet real scalar field. Our focus is on theories with an approximate and spontaneously broken $\mathbb{Z}_2$ symmetry where quasi-stable domain walls can form at early times. This seemingly simple framework bears a wealth of phenomenological implications that can be tackled by means of different cosmological and astrophysical probes. We elucidate the connection between domain wall dynamics and the production of dark matter and gravitational waves. In particular, we identify three main benchmark scenarios. The gravitational wave signal observed by pulsar timing arrays can be generated by the domain walls if the mass of the singlet is $m_s \sim\,$PeV. For lower masses, but with $m_s \gtrsim 10\,$GeV, scalars produced in the annihilation of the domain walls can be dark matter with a distinctive feature in their power spectrum. Finally, the thermal bath provides an unavoidable source of unstable scalars via the freeze-in mechanism whose subsequent decays can be tested by their imprints on cosmological and terrestrial observables.

Figures (4)

• Figure 1: An illustration of the scalar potential for $S$ in the limit when the portal quartic interaction with the SM Higgs doublet is suppressed, $\lambda_P \ll 1$. The dashed line shows the $\mathbb{Z}_2$-symmetric contribution whereas the solid line includes the bias term $\mu_3 = 0.05 \, \lambda_S v_S$ (we set $\mu_1 = 0$). The constant $V_0$ is set to have a vanishing potential when the scalar field sits at the positive minimum, $V(v_S > 0) = 0$.
• Figure 2: Left panel: Absolute value of the mixing angle $\theta$ as a function of $m_s$ needed to ensure that the mostly-singlet $s$ lifetime equals the present age of the Universe. The vertical dashed lines identifies the masses where some decay channels open up. Right panel: Branching ratios of $s$ in the small mixing angle limit.
• Figure 3: Left panel: The projected sensitivities (${\rm SNR}>8$) of LISA, AEDGE and ET on GW background generated by DWs in the real scalar singlet model with $\lambda_S = 0.1$. The vertical dashed contours indicate the peak frequency of the GW signal, $f_p\propto T_{\rm ann}$. Along the solid black line, the observed DM abundance in $s$ is generated from DW annihilation and the region above it is excluded by DM overproduction if $s$ is quasi-stable. The gray region is excluded by constraints from CMB and BBN on the total abundance of GWs and in the thermal DW scenario the DWs form only in the region above the dashed brown line. Right panel: A zoom of the left panel in the region of the PTA fit.
• Figure 4: Summary plot in the $(m_s, |\theta|$) plane at fixed $\lambda_S = 0.1$. The orange curves show isocontours of constant lifetime $\tau_s$. Along the black dashed curve, the freeze-in abundance of $s$ would equal the observed DM abundance if $s$ was stable, and above the black dotted curve $s$ thermalizes with the SM bath. The gray region is excluded by the invisible decays of the Higgs boson. In the purple region, the $s$ mass is in the range where the DW annihilation can generate the GW background observed by the PTAs and $s$ decays before BBN. In the green region $s$ lifetime exceeds the constraints arising from X-ray, CMB, $\gamma$-ray and radio observations and $s$ can constitute DM. The red dashed vertical lines identify DM lower mass bounds: the DW annihilation happens before matter radiation equality $T_{\rm eq}$, and before the temperature $T_{{\rm Ly}\alpha}$ when the scales relevant for the Lyman-$\alpha$ forest constraints re-enter the horizon. Finally, the unavoidable freeze-in production puts the following bounds: the blue region is excluded by the BBN constraints, the turquoise regions are excluded by the constraints from CMB anisotropies (lighter) and spectral distortions (darker), the brown region is excluded by X-ray constraints.