Decaying vector dark matter with low reheating temperature for KM3NeT signal and its impact on gravitational waves

TL;DR

This work presents a decaying super-heavy dark matter framework from a $U(1)_D$-extended SM with a SM-singlet scalar, where a low reheating temperature provides entropy dilution to reconcile heavy DM with the observed relic density. The DM candidate $W_D$ decays through kinetic mixing, producing neutrinos and other SM particles, and a portion of the DM density can explain the KM3NeT signal without conflicting IceCube data. Concurrently, cosmic strings from $U(1)_D$ breaking generate a GW spectrum that can be detectable in future experiments, with a characteristic suppression at high frequencies due to the nonstandard reheating dynamics $a\propto T^{-3/8}$. Together, the neutrino-flux and GW signatures offer a coherent, testable link between high-energy particle physics and early-Universe cosmology, with collider-accessible Higgs sector parameters and distinctive GW footprints offering avenues for verification.

Abstract

We propose a new model to explain the KM3NeT neutrino event through a low reheating scenario with a suppression in the GW spectrum originating from cosmic string networks. To achieve this, we extend the SM gauge sector by an abelian gauge symmetry and a singlet scalar. Once the abelian gauge symmetry spontaneously breaks, the extra gauge boson acquires mass and becomes a suitable Dark Matter (DM) candidate. Due to the kinetic mixing with the hypercharge gauge group, DM can decay into SM particles. To explain the KM3NeT signal, we need $\mathcal{O}(100)$ PeV DM, which can be produced in the correct order of DM density in a low reheating scenario. In this scenario, the overabundance issue of heavy DM can be tackled by diluting its abundance through the continuous injection of entropy when the matter-like inflaton decays into the SM bath. Using the low reheating scenario, we can obtain the correct value of DM density both for freeze-out and freeze-in mechanisms for super-heavy DM. Moreover, we have studied the Gravitational Waves (GWs) produced from cosmic strings, which fall within the detectable range of future proposed GW experiments. Additionally, the dominance of a quadratic inflaton potential before the reheating temperature changes the temperature-scale factor relation, which suppresses the GW spectrum at higher frequencies. Choosing an arbitrarily low reheating temperature provides only a tiny fraction of the DM density due to dilution from entropy injection. This fraction of the vector DM suggests that only the extragalactic contribution is relevant in the KM3NeT event because DM lifetime is shorter than the age of the Universe.

Figures (11)

• Figure 1: Variation of DM relic density with the DM mass for three different values of the gauge coupling. The shaded violet region denotes the DM mass range that can explain the KM3NeT signal. Dashed magenta line correspond to the DM relic density from Planck data, $\Omega_{\rm DM}h^2=0.12$.
• Figure 2: LP shows DM production via the freeze-out mechanism, and RP shows DM production via the freeze-in mechanism in the low reheating scenario. Both plots are presented for three different values of the inflaton decay width $\Gamma_{\rm inf}$. The other parameter values have been kept fixed for LP (RP) at $\sin\alpha = 0.1$, $M_{h_2} = 300$ GeV, $g_{D} = 2.0$ ($g_{D}=0.1$), and $H_{I} = 10^{11}$ GeV.
• Figure 3: LP and RP show the variation of DM relic density with the gauge coupling for three values of the inflaton decay width $\Gamma_{\rm inf}$ and DM mass $M_{W_D}$, respectively. The solid line shows DM production via the freeze-in mechanism, corresponding to FIMP-type DM, while the dashed line shows the freeze-out mechanism, corresponding to WIMP-type DM. The other parameter values have been kept fixed at $M_{h_2} = 300$ GeV, $M_{W_D} = 4.4 \times 10^{8}$ GeV, $g_{D} = 2$, $\Gamma_{\rm inf}=3.38 \times 10^{-8}$ GeV, $\sin\alpha=0.1$, and $H_{0} = 10^{11}$ GeV, unless the parameters are varied.
• Figure 4: In both plots, we show the variation of DM with the inflaton decay width. In the LP, the results are shown for three values of the gauge coupling $g_{D}$, whereas in the RP, they are shown for three values of the DM mass $M_{W_D}$.
• Figure 5: The LP and RP show the variation of DM relic density with the DM mass for three values of the inflaton decay width $\Gamma_{\rm inf}$ and the gauge coupling $g_D$, respectively.