Preheating in Supersymmetric Hybrid Inflation

TL;DR

This work analyzes preheating after inflation in a class of supersymmetric hybrid inflation models, highlighting how a single SUSY coupling produces one dominant oscillation frequency and how mixing among the homogeneous fields can drastically alter particle production. The authors develop a general multi-field preheating framework and apply it to a $\phi$NMSSM-inspired scenario with an approximate Peccei-Quinn symmetry to study axion production and backreaction. They show that mixing enhances the production of the dominant real scalars $\phi$ and $N$, while backreaction quickly halts tachyonic growth and suppresses axion production, keeping axions within experimental bounds. The results imply efficient preheating in these SUSY setups and clarify the role of backreaction in determining the post-inflationary particle content and energy transfer.

Abstract

We study preheating in a general class of supersymmetric hybrid inflation model. Supersymmetry leads to only one coupling constant in the potential and thus only one natural frequency of oscillation for the homogeneous fields, whose classical evolution consequently differs from that of a general (non-supersymmetric) hybrid model. We emphasise the importance of mixing effects in these models which can significantly change the rate of production of particles. We perform a general study of the rate of production of the particles associated with the homogeneous fields, and show how preheating is efficient in producing these quanta. Preheating of other particle species will be model dependent, and in order to investigate this we consider a realistic working model of supersymmetric hybrid inflation which solves the strong-CP problem via an approximate Peccei-Quinn symmetry, which was proposed by us previously. We study axion production in this model and show that properly taking into account the mixing between the fields suppresses the axion production, yet enhances the production of other particles. Finally we demonstrate the importance of backreaction effects in this model which have the effect of shutting off axion production, leaving the axion safely within experimental bounds.

Figures (14)

• Figure 1: Oscillations of the classical fields (left) and the trajectory in the $N-\phi$ plane (right). The top panels correspond to the supersymmetric hybrid model with $\phi_c=10^{16}\, GeV$, $\kappa=10^{-3}$ and $m_\phi=3.7\times 10^{9}\, GeV$. The time scale is given in terms of the approximate number of oscillations of the fields, $N'=\bar{m}_\phi t /2 \pi$, where $N'=0$ has been defined for convenience as the point where the fields reach the first peak. The lower panels show for comparison the situation in a non-supersymmetric hybrid model with $g= \sqrt{\lambda} = 10^{-3}$, and $\phi_c (=\Lambda)$ and $m_\phi$ as before.
• Figure 2: The trajectories through the Mathieu stability/instability chart for $\textbf{k}=0$ showing how the efficiency of parametric resonance varies over each stage in the classical field oscillation. The contours are incremented in levels of $\mu\sim 0.1$, ranging from the darkly shaded (stable) regions to the light (extremely unstable) regions. Modes $\textbf{k}> 0$ will lie vertically above the zero mode trajectories shown. Particle production occurs mostly in the second instability band.
• Figure 3: The growth index $\mu(A,q)$ for the static Mathieu Equation.
• Figure 4: Initial rates of production of $\phi$ and $N$ particles for the model with $\kappa=10^{-3}$, $\phi_c= 10^{16}\, GeV$ and $m_\phi= 3.7 \times 10^{9} \, GeV$. In the left side plot the results without taking into account the mixing term in the effective squared mass matrix are displayed; we have also included the oscillation of the classical field $N(t)$ (dashed line) scaled by a factor of 5. The comoving momentum $k$ is given in both plots in units of the natural frequency $\bar{m}_\phi$ and it corresponds to the physical momentum at $N' \approx -17$. In the right side plot, by the time particles are produced the initial value of the physical momentum $k/a=0.7 \bar{m}_\phi$ has been red-shifted below $0.58 \bar{m}_\phi$.
• Figure 5: Classical trajectory in field space ($\phi,N$) after inflation, (for the parameters given in (\ref{['params']})) in the case of both hybrid and inverted hybrid inflation. The fields begin at $\phi=(1 \pm 1/\sqrt{2})\phi_0, N=0$, and oscillate around $\phi=\phi_0, N=N_0$, where, neglecting particle production, they eventually settle.