Complementarity between Cosmic String Gravitational Waves and long-lived particle searches in a laboratory

TL;DR

Networks of cosmic strings emit a stochastic gravitational-wave background that is nearly flat during radiation domination, but an early matter-dominated epoch (EMD) driven by a metastable long-lived particle leaves a characteristic turnover at $f_{ m brk}$ in the spectrum. The authors propose a concrete $U(1)$-extended dark sector with a Higgs-portal scalar $S$ that can drive EMD, and they analyze both freeze-out and freeze-in production as well as nonzero initial abundances to connect GW spectral features with laboratory observables. By combining gravitational-wave detectors (LISA, ET, $\mu$Ares) with LLP searches (DUNE, FASER, MATHUSLA, SHiP), they show regions of parameter space where $m_S$, $\sin\theta$, and $\Gamma_S$ can be probed cosmologically and in the lab, with distinct footprints for local versus global strings. The results demonstrate that freeze-in scenarios can extend the accessible parameter space to GeV-scale $m_S$, yielding detectable GW turns and LLP signals, and highlight a general strategy to use cosmological GW signatures to guide terrestrial experiments in probing nonstandard cosmologies. This synergy offers a powerful route to constrain high-scale physics and the nature of the dark sector.

Abstract

Cosmic strings are powerful witnesses to cosmic events including any period of early matter domination. If such a period of matter domination was catalysed by metastable, long-lived particles, then there will be complementary signals to ascertain the nature of dark sector in experiments detecting primordial features in the gravitational wave (GW) power spectrum and laboratory searches for long-lived particles. We give explicit examples of global and local U(1) gauge extended dark sectors to demonstrate such a complementarity as the union of the two experiments reveals more information about the dark sector than either experiment. Demanding that Higgs-portal long-lived scalar be looked for, in various experiments such as DUNE, FASER, FASER-II, MATHUSLA, SHiP, we identify the parameter space which leads to complementary observables for GW detectors such as LISA and ET.

Figures (6)

• Figure 1: Schematic timeline of key events: Following inflation, a $(B-L)$ phase transition generates cosmic string networks during the early radiation-dominated (ERD) era, which become a dominant source of GWs primarily through loop production. Simultaneously, a real scalar singlet, $S$, acquires a mass dependent on the $(B-L)$ Higgs vacuum expectation value. Starting from $H_{\rm EMD}$ to $\Gamma_S$, this scalar dominates the universe's energy density, after which the universe transitions to standard radiation domination. The long-lived scalar leaves an imprint on the high-amplitude GWs generated by cosmic strings, with the duration ($N_e$) and end of matter domination ($\Gamma_S$) influencing the spectral shapes, which would otherwise produce a scale-invariant, flat plateau at high frequencies. Upcoming beam dump experiments offer a compelling and complementary approach to search for and constrain such long-lived BSM particles based on their mass ($m_S$) and decay width ($\Gamma_S$) to the SM states.
• Figure 2: Complementarity of GW and laboratory searches (indicated by colored dots) for Top-left: standard non-relativistic FO with local $(B-L)$ strings with $v_{\rm CS}=10^{14}$ GeV, Top-right: standard non-relativistic FO with global $(B-L)$ strings with $v_{\rm CS}=10^{15}$ GeV, Bottom-left: standard FI with $H_i=10^8$ GeV and local $(B-L)$ strings with $v_{\rm CS}=10^{14}$ GeV, Bottom-right: standard FI with $H_i=10^8$ GeV and global $(B-L)$ strings with $v_{\rm CS}=10^{15}$ GeV. The colored shaded regions represent the sensitivity curves of various GW experiments, such as $\mu$Ares (red), LISA (blue), DECIGO (green), and ET (brown), with the stipulation that the first turning point frequency to be detected with SNR $>10$. The gray shaded regions are excluded by CHARM, LHCb, CMS re-interpretation results. The solid lines show the sensitivity of upcoming long-lived particle searches like DarkQuest1, DarkQuest2, MATHUSLA, SHiP, etc.
• Figure 3: Complementarity of GW and laboratory searches with a non-zero initial $S$- abundance(indicated by colored dots) for Top-left: freeze-in with local $(B-L)$ strings with $v_{\rm CS}=10^{14}$ GeV, initial Hubble scale $H_i=10^{12}$ GeV and $\eta_S=10^{-15}$, Top-right: same as the earlier with global $(B-L)$ strings with $v_{\rm CS}=10^{15}$ GeV, Bottom-left: freeze-in with local $(B-L)$ strings with $v_{\rm CS}=10^{14}$ GeV, initial Hubble scale $H_i=10^{12}$ GeV and $\eta_S=10^{-13}$, Bottom-right: same as the earlier with global $(B-L)$ strings with $v_{\rm CS}=10^{15}$ GeV. As above, the shaded regions correspond to the ability of a GW detector to "see" the end of matter domination.
• Figure 4: Complementarity of GW and colliders dedicated for higher mass searches with a significantly larger initial $S$- abundance(indicated by colored dots) for Left: freeze-in with local $(B-L)$ strings with $v_{\rm CS}=10^{14}$ GeV, initial Hubble scale $H_i=10^{12}$ GeV and $\eta_S=10^{-5}$, Right: same as the earlier with global $(B-L)$ strings with $v_{\rm CS}=10^{15}$ GeV. As above, the shaded regions correspond to the ability of a GW detector to "see" the end of matter domination.
• Figure 5: Imprints of long-lived scalar $S$ on SGWB from cosmic strings and complementarity with collider searches for the benchmarks BP1 ("$\star$"), BP2 "$\spadesuit$"), BP3 "$\clubsuit$") (see Table-\ref{['t1']}) shown in left: for local strings, right: for global strings. As above, for both plots, the shaded regions correspond to the ability of a GW detector to "see" the end of matter domination.