Gravitational Wave Signatures from Lepton Number Breaking Phase Transitions with Flat Potentials

TL;DR

Addresses gravitational wave signals from first-order phase transitions tied to lepton-number breaking with flat potentials, where thermal corrections generate barrier structures. Develops a finite-temperature effective potential V_eff(Φ,T) = V_Tree + V_CW + V_T + V_Daisy and analyzes U(1) and SU(2) extensions in SU(2)→U(1) and SU(2)→1 breakings, showing barrier strength scales with the UV cutoff m_X. Predicts GW spectra using α and β/H defined by $α = \Delta V / ρ_{rad}$ and $β/H_* = [T \; d/dT (S_3/T)]|_{T=T_n}$, finding parameter regions where $Ω_{GW} h^2$ falls within LISA/DECIGO/BBO sensitivity. Links neutrino mass generation via the seesaw to gravitational wave observables and outlines multi-messenger strategies and theoretical challenges for modeling strong transitions and EFT validity.

Abstract

Extensions of the Standard Model typically contain ``flaton fields" defined as fields with large vacuum expectation values and almost flat potentials where scalar self-coupling is small or vanishes at tree level. Such potentials have been used to drive a secondary inflationary epoch after a primary phase of inflation, in what are called thermal inflation models. Although the primordial, high-scale inflationary epoch can solve the horizon and flatness problems, it does not always resolve difficulties associated with late-time relics produced in extensions of the Standard Model. These relics typically decay too late, injecting entropy and energetic particles that spoil successful predictions like Big Bang Nucleosynthesis. It is here that thermal inflation plays a crucial role: diluting unwanted relics by many orders of magnitude without erasing the baryon asymmetry or the large-scale structure set up by the earlier phase of inflation. The preferred scale for this phenomenon is in the range $10^6-10^8$ GeV if one considers supergravity, but without it, any scale above the EW scale is valid. We investigate a typical form of these potentials and determine what are the conditions for the potentials to develop a barrier such that when the flatons settle to the true minimum, the associated Gravitational Waves can be observed.

Figures (10)

• Figure 1: U(1) symmetry breaking potentials for various $m_X$ values with coupling parameters $g=0.3$ and $\lambda=0.8$, for a fixed value of $m_0=10^4$ GeV. Left: tree-level potential $V(\phi)/v^4$ versus $\phi/v$ for $m_X = 10^7$, $10^8$, and $10^9$ GeV, illustrating how the potential flattens as $m_X$ increases. Right: Total effective potential at the critical temperature $T_c$, demonstrating that larger $m_X$ values produce higher and wider potential barriers. Here, $v$ denotes the vacuum expectation value of the tree-level potential. The two plots have been rendered in different scales, due to the size of the loop and thermal contributions.
• Figure 2: Left: $SU(2)$ symmetry partially breaking potentials for different $m_X$ with coupling parameters $g=0.3$, $m_0=10^4$ GeV, and $\lambda=0.8$ and $n_f=0$. Total effective potential at critical temperature $T_c$, showing how increasing $m_X$ leads to higher and wider potential barriers. Right: $SU(2)$ symmetry maximally breaking potential for different $m_X$ with coupling parameters $g=0.3$ and $\lambda=0.8$, for this case also $n_f=0$. The effective thermal potential is shown at the critical temperature $T_c$, showing how increasing $m_X$ leads to higher and wider potential barriers. In both cases, $v$ is the vacuum expectation value of the tree-level potential.
• Figure 3: Phase transition parameters for $U(1)$ symmetry breaking in the $(g, \lambda)$ parameter space and the corresponding GW density. Left: At $m_X = 10^7$ GeV, and $n_f=0$, showing contours for $\alpha$ (solid lines) and $\beta/H_*$ (dashed lines). Right: At $m_X = 10^9$ GeV, contours for $\alpha$ and $\beta/H_*$. The color gradient indicates the corresponding GW density.
• Figure 4: Comparison of scan results for different $n_f=0$ (left) and $n_f = 6$, $y = 0.35$ (right) values, for the case of the breaking $SU(2)\rightarrow U(1)$.
• Figure 5: Comparison of scan results for different $n_f$ and $y$ values.