Superheavy dark matter production from a symmetry-restoring first-order phase transition during inflation

We propose a scenario where superheavy dark matter (DM) can be produced via symmetry restoration first-order phase transition during inflation triggered by the evolution of the inflaton field. The phase transition happens in a spectator sector coupled to the inflaton field. During the phase transition, the spectator field tunnels from a symmetry-broken vacuum to a symmetry-restored vacuum. The massive particles produced after bubble collisions are protected against decaying by the restored symmetry and may serve as a DM candidate in the later evolution of the Universe. We show that the latent heat released during the phase transition can be sufficient to produce the DM relic abundance observed today. In addition, accompanied with the super heavy DM, this first-order phase transition also produces gravitational waves detectable via future gravitational wave detectors.

Figure 1

The potential shape $V(\varphi ,\sigma )$ and the field trajectory. The magenta, cyan, and green curves show the plane sections along the $\sigma$ direction. The inflaton rolls down along the $\varphi$ direction due to a slow-roll potential. Initially, the field follows the false vacuum (red). Then as the true vacuum (blue) forms and becomes lower than the false vacuum, the $\sigma$ field tunnels through the barrier (black dashed line) and triggers the SRFOPT.

Figure 2

The diagrams that contribute to the decreasing in the number of the $\sigma$ field.

Figure 3

$Y_{\sigma }(\infty )$ as a function of $H$ for different values of $\mathcal{C}$. Here the value of $L/{\rho }_{\inf }$ is fixed to be 0.1.

Figure 4

The frequency of the highest peak of the GW spectrum today produced by SRFOPT during inflation as function of $H$ for various values of $L/{\rho }_{\inf }$. The relic energy density of ${\rho }_{\mathrm{DM}}$ is fixed to today’s observed value. The collision parameter $\mathcal{C}$ in Eq. (32) is fixed to 0.01. Sensitive regions of future space GW detectors and pulsar timing arrays are also shown by the shaded regions.

Figure 5

The upper figure shows the gravitational wave signal associated with the SRFOPT for different superheavy dark matter mass and different $e$-folding number before the end of inflation. The thickest line corresponds to $L/{\rho }_{\inf }=0.3$ and the think line corresponds to $L/{\rho }_{\inf }=0.1$. The lower figure shows the gravitational wave signature for different universe evolution scenarios. The thickest line denotes the case of instantaneous reheating, the second thickest line denotes the case of kination domination immediately after the end of inflation, the thinnest line denotes the case of matter domination immediately after the end of inflation. In the $\tilde{p}=1/3$ and $\tilde{p}=2/3$ case, we used ${\tau }_r/|{\tau }_{\mathrm{PT}}|=10$. In both figures, for the three cases, we take $N_{\mathrm{PT}}=18.6,m_{\sigma }=170H,H={10}^{14}\mathrm{GeV}$ for the brown curve, $N_{\mathrm{PT}}=15,m_{\sigma }=5\times {10}^{6}H,H={10}^5\mathrm{GeV}$ for the blue curve and $N_{\mathrm{PT}}=7.8,m_{\sigma }=1.7\times {10}^{16}H,H={10}^{-15}\mathrm{GeV}$ for the red curve. We choose the parameters $N_{\mathrm{PT}}$ and $m_{\sigma }$ such that the SRFOPT can produce just enough $\sigma$ field to explain the DM relic abundance today. The other parameters are chosen to be $\beta =5H$, $\lambda =-1$, ${\gamma }_{\mathrm{PT}}=0.6$ and $\mathrm{\Lambda }=2m_{\sigma }$ when making this plot. The experiments are LISA [76], eLISA [77], DECIGO [78], UDECIGO [79], BBO1 [80], BBO2 [81], TianQin [82] and Taiji [83], ET [70], and CE [84].

Figure 6

The magnitude estimation of different elements that will contribute to the scattering amplitude in the model. We can use it to estimate the dominant processes that contribute to DM reduction.

Figure 7

This figure shows the evolution of DM comoving particle number density after considering its interactions. The parameters are chosen as $\lambda =-1$, ${\gamma }_{*}=0.01$ and $\mathrm{\Lambda }=2m_{\sigma }$ when making this plot.