SUSY breaking by a metastable ground state: Why the early Universe preferred the non-supersymmetric vacuum

TL;DR

This work shows that in ISS-based models, finite-temperature cosmology naturally drives the early Universe toward a metastable, non-supersymmetric vacuum because it hosts more light degrees of freedom than the SUSY-preserving vacua. The authors derive the finite-temperature effective potential, identify critical temperatures for classical and quantum transitions, and establish a reheating-temperature window $T_{\rm degen} < T_R \lesssim T_*$ (equivalently $\mu/\epsilon^{1-2N/(N_f-N)} \lesssim T_R \lesssim \mu/\epsilon$) within which the Universe ends in the SUSY-breaking vacuum. They further show that after nucleation or rolling, damping and couplings to the messenger sector trap the field at the metastable minimum as the Universe cools, thereby offering a natural cosmological explanation for SUSY breaking. A key result links the SUSY-breaking scale to the reheating temperature via $\mu \sim \Lambda_L (T_R/\Lambda_L)^{(N_f-N)/(2N)}$, constraining high-scale realizations and connecting early-universe dynamics to low-energy SUSY phenomenology.

Abstract

Supersymmetry breaking in a metastable vacuum is re-examined in a cosmological context. It is shown that thermal effects generically drive the Universe to the metastable minimum even if it begins in the supersymmetry-preserving one. This is a generic feature of the ISS models of metastable supersymmetry breaking due to the fact that SUSY preserving vacua contain fewer light degrees of freedom than the metastable ground state at the origin. These models of metastable SUSY breaking are thus placed on an equal footing with the more usual dynamical SUSY breaking scenarios.

Figures (3)

• Figure 1: Zero temperature effective potential $\hat{ V}_{T=0} (\gamma)$ of Eq. \ref{['VzeroT']} as a function of $\gamma = \Phi/\mu.$ For the SUSY preserving vacuum $|{\rm vac}\rangle_0$ we chose $\gamma=\gamma_0=7.5$. The SUSY breaking metastable minimum $|{\rm vac}\rangle_+$ is always at $\gamma=0,$ and the top of the barrier is always at $\gamma=1.$ We have taken the minimal allowed values for $N$ and ${N_{f}}$, $N=2$, ${N_{f}}=7.$
• Figure 2: Thermal effective potential \ref{['Vth2']} for different values of the temperature. Going from bottom to top, the red line corresponds to the temperature $\Theta \gtrsim \Theta_{\rm crit}$ where we have only one vacuum at $\gamma=0$. The orange line corresponds to $\Theta\approx \Theta_{\rm crit}$ where the second vacuum appears and the classical rolling stops. The green line is in the interval $\Theta_{\rm degen} < \Theta < \Theta_{\rm crit}$ where one could hope to tunnel under the barrier. The blue line is at $\Theta \sim \Theta_{\rm degen}$ where the two vacua become degenerate. Finally, the black line gives the zero temperature potential where the non-supersymmetric vacuum at the origin becomes metastable.
• Figure 3: A simple no-barrier model for the thermal effective potential. The modelling potential $\hat{V}_{\rm lin}(\gamma)$ is shown in red and the exact thermal potential $\hat{V}_{T}(\gamma)$is black. The tunnelling rate to the true vacuum for this model is calculated in the text.