Dark, Cold, and Noisy: Constraining Secluded Hidden Sectors with Gravitational Waves

TL;DR

Addressing the challenge of probing secluded hidden sectors, the paper studies gravitational waves from first-order phase transitions occurring in sectors possibly at sub-MeV temperatures and with different temperatures from the SM. It develops a model-independent framework to connect PT dynamics (\alpha, \beta/H, T_{\text{nuc}}) and temperature ratios to GW spectra, and then assesses detectability across current and future detectors, including PTAs. Two minimal benchmark models—the singlet-scalar sector and a spontaneously broken U(1)' dark gauge sector—illustrate the range of possible signals under cosmological constraints on $N_{\text{eff}}$. The results show that observable signals are possible only for low nucleation temperatures and not-too-small hidden-sector temperatures, or for very near-future missions; cosmological constraints strongly restrict viable parameter space, especially for fully decoupled sectors.

Abstract

We explore gravitational wave signals arising from first-order phase transitions occurring in a secluded hidden sector, allowing for the possibility that the hidden sector may have a different temperature than the Standard Model sector. We present the sensitivity to such scenarios for both current and future gravitational wave detectors in a model-independent fashion. Since secluded hidden sectors are of particular interest for dark matter models at the MeV scale or below, we pay special attention to the reach of pulsar timing arrays. Cosmological constraints on light degrees of freedom restrict the number of sub-MeV particles in a hidden sector, as well as the hidden sector temperature. Nevertheless, we find that observable first-order phase transitions can occur. To illustrate our results, we consider two minimal benchmark models: a model with two gauge singlet scalars and a model with a spontaneously broken $U(1)$ gauge symmetry in the hidden sector.

Figures (11)

• Figure 2: Noise curves (left) and PLI sensitivity curves (right) for various gravitational wave observatories. Dashed black lines in the left-hand plot indicate the expected magnitude of several important backgrounds, in particular super-massive black hole binaries (SMBHB) Simon:2016ibtArzoumanian:2018saf, and galactic Cornish:2017vipCornish:2018dyw as well as extra-galactic Farmer:2003paYagi:2011yu compact binaries (CB). In determining the power-law integrated sensitivity curves (as well as in the toy model analyses presented in \ref{['sec:toymodels']}), we assume that the SMBHB background will eventually be resolvable, while the CB background will remain unresolved. In the right-hand plot, we also show example spectra generated by a phase transition at $T^\text{nuc}=10GeV$ and with $\alpha=0.1$, $\beta/H=10$ for both runaway and non-runaway bubbles. The parameter choices made for forthcoming experiments are given in \ref{['sec:appendix-sensitivity']}, and the data underlying our noise curves and PLI sensitivity curves can be found in the ancillary material.
• Figure 3: Anticipated sensitivity to hidden sector phase transitions for various future gravitational wave observatories. In the left-hand panels we assume runaway bubbles, while the right-hand panels show the case of non-runaway bubbles. We show the sensitivities as a function of the hidden sector temperature at which bubble nucleation occurs, $T_h^\text{nuc}\xspace$, versus the transition strength $\alpha$ (top), the inverse time scale $\beta/H$ (middle), and the temperature ratio between the hidden and visible sector $\xi_{h}\xspace$ (bottom). In all panels, we have assumed $g_{h}\xspace \ll g_{\star,\text{SM}}\xspace$ in calculating the redshifting of gravitational wave spectra. Note that in the bottom panel, we fix $\alpha_h$ (the value of $\alpha$ at $\xi_{h}\xspace = 1$) instead of $\alpha$ to explicitly show the $\xi_{h}\xspace$-dependence of $\alpha$ for fixed values of $T_h^\text{nuc}$. Note that the translation of $\alpha_h$ to the physical $\alpha$ also relies upon the assumption $g_{h}\xspace \ll g_{\star,\text{SM}}\xspace$. \ref{['fig:max_hidden_dofs']} shows the resulting sensitivity when this assumption is relaxed. The discontinuities in the lower panel (best visible for SKA) originate from a step-function approximation to $g_{\star,\text{SM}}\xspace$.
• Figure 4: Requirements for observable gravitational wave signals from a phase transition in a fully decoupled hidden sector in terms of the nucleation temperature and the number of relativistic degrees of freedom at BBN. Models within the purple shaded region saturate the BBN constraints on $N_\text{eff}$ (see \ref{['eq:Neff-dec']}) and yield a gravitational wave signal observable in SKA. The left-hand (right-hand) panel corresponds to runaway (non-runaway) bubble walls. The gray shaded region indicates that the phase transition occurs before the onset of BBN, alleviating any constraints on the maximal number of degrees of freedom.
• Figure 5: Qualitative behavior of the effective potential $V_\text{eff} (S,T)\simeq V_\text{tree}(S)+V_T(S,T)$ in the singlet scalar model without an auxiliary scalar field $A$ ($\lambda_{SA}=\kappa_{SA}=0$, left panel) and with the inclusion of such a field ($\lambda_{SA},\kappa_{SA}>0$, right plot). Only in the latter case is a first-order phase transition realized. For illustration purposes we have shifted the potentials such that $V_\text{eff}(0,T)=0$.
• Figure 6: The strength of the hidden sector phase transitions $\alpha$ (left panel) and its inverse time scale $\beta/H$ (right panel) for the singlet scalar model given by \ref{['eq:Vtree-scalar']} at the scale $T_h^\text{nuc}\xspace\sim v_S^0 = 50keV$. Inside the regions bounded by the black lines, the gravitational wave signals from the phase transition will be detectable by SKA after the indicated periods of observation time. To satisfy the cosmology constraints for $v_S^0 = 50keV$, we require the hidden sector to be colder than the visible sector by a factor of $\xi_{h}\xspace = 0.66$ at the time of the transition. This is the temperature ratio that arises naturally in our $\nu$-quilibration scenario (see \ref{['eq:xi-reeq-1', 'eq:Neff-reeq-2']}), satisfying the CMB+$H_0$ cosmology constraint given in \ref{['eq:Neff-constraint-CMB-H0']}.