Inflaton Decay and Heavy Particle Production with Negative Coupling

TL;DR

This work addresses reheating after chaotic inflation in a two-field scalar theory by focusing on a negative cross-coupling $g<0$ between the inflaton and a second scalar. It combines lattice simulations of the nonlinear classical equations of motion with analytical stability analyses to uncover a negative coupling instability that dramatically enhances heavy particle production and accelerates inflaton decay, particularly for $m_ ext{χ} oughly 10^{14}$ GeV, within natural couplings. A key contribution is the demonstration that negative coupling opens a broad, efficient production channel for heavy bosons and supports a viable GUT baryogenesis scenario, aided by a simple toy model linking preheating dynamics to $n_B/s$ that is largely insensitive to decay rates in the massless-inflaton limit. The results highlight the importance of backreaction, the scattering regime, and phase dynamics in determining maximum field variances and particle production, offering a promising mechanism for baryogenesis during preheating with natural parameter values.

Abstract

We study the decay of the inflaton in a renormalizable two scalar theory. Since the dynamics of the system is dominated by states with large occupation numbers which admit a semiclassical description, the decay can be studied by solving the classical equations of motion on the lattice. Of particular interest is the case when the cross-coupling between the inflaton and the second scalar field is negative, which is naturally allowed in many realistic models. While the inflaton decays via parametric resonance in the positive coupling case we find that for negative coupling there is a new mechanism of particle production which we call negative coupling instability. Due to this new mechanism the variances of the fields grow significantly larger before the production is shut off by the backreaction of the created particles. We also find that heavy particles are produced much more efficiently with negative coupling, which is of prime importance for GUT baryogenesis. Using a simple toy model for baryogenesis and the results of our lattice simulations we show that for natural values of the cross-coupling enough 10^{14}GeV bosons are created to produce a baryon to entropy ratio consistent with observation. For positive coupling the value of the cross-coupling required to produce such massive particles is unnaturally large. In addition to our numerical results we obtain analytical estimates for the maximum variances of the fields in an expanding universe for all cases of interest in our model.

Figures (19)

• Figure 1: (a) : The stability chart of the Mathieu equation, Eq. (\ref{['eq:mathieu']}). The dark regions correspond to stable solutions while the light regions correspond to exponential instabilities. We also show contours of constant $\mu$, where $\mu$ is the instablity index. The curve $\mu=0$ divides the parameter space into stable and unstable regions. The contours shown are $\mu=$ {0, 0.1, 0.2, 0.3, 0.5, 1.0, 2.0, 3.0}. The lines $A_0=2|q_0|$ and $A_0=-2|q_0|$ are also plotted. (The plot was generated numerically, and in order to keep the file size small we used a fairly coarse grid. The instability bands really extend all the way to $q_0=0$ at the points $A_0=n^2$, $n=1,2,3,\dots$. Also, for negative $A_0$ the narrow regions of stability form continuous bands rather than the "island" structure shown.)
• Figure 1: (b) : The stability chart of the Mathieu equation for large $A_0$ and $q_0$. As in figure 1(a) the dark regions correspond to stable solutions while the light regions correspond to exponential instabilities. The contours shown are $\mu=$ {0, 0.1, 0.2, 0.3, 0.5, 1.0 }, and the line $A_0=2|q_0|$ is also plotted. Notice that the distance between resonance bands above $A_0=2|q_0|$ for fixed $q_0$ is $\delta A_0 \approx |q_0|^{1/2}$. Notice also that the instability index $\mu$ decreases rapidly with increasing $A_0$.
• Figure 2: The expectation values of the fields as a function of time for negative coupling, $|q_0|\approx 35$, $r=10$ ($m_\chi = m_\phi = 0$, $\lambda_\phi=10^{-12}$, $\lambda_\chi=10^{-7}$, $g=-10^{-10}$).
• Figure 3: The expectation values of the fields as a function of time for positive coupling, $q_0\approx 35$, $r=10$ ($m_\chi = m_\phi = 0$, $\lambda_\phi=10^{-12}$, $\lambda_\chi=10^{-7}$, $g=10^{-10}$).
• Figure 4: The variances of the fields as a function of time for negative coupling, $|q_0|\approx 35$, $r=10$ ($m_\chi = m_\phi = 0$, $\lambda_\phi=10^{-12}$, $\lambda_\chi=10^{-7}$, $g=-10^{-10}$).