Dynamical Evolution and Graceful Exit in Quartic Warm Inflation

TL;DR

The paper addresses whether warm inflation driven by a quartic potential can gracefully exit to a radiation-dominated Universe under a temperature-dependent dissipation coefficient. It solves the full nonlinear dynamics of the coupled system for inflaton energy density $u$, radiation energy density $\rho$, and expansion rate $H$ with $V(\phi)=1/4\,\lambda\phi^4$ and $\Gamma=aT$, avoiding slow-roll approximations. The authors find that in the weak regime radiation domination is suppressed, while in the strong regime the Universe transitions to radiation domination within about four e-folds after inflation ends, with reheating temperatures around $T_{end}\sim 10^{13}$ GeV and $T_{eq}\sim 10^{12}$ GeV. This work confirms graceful exit in quartic warm inflation and demonstrates that nonlinear dynamics are essential to capture the transition, while remaining compatible with Planck constraints.

Abstract

In this study, we investigate the full nonlinear dynamics of warm inflation driven by the quartic inflaton potential, avoiding any simplifying approximations. The thermal backreaction is incorporated through a dissipation coefficient that depends linearly on the temperature, and the model parameters are chosen to remain consistent with Planck observational constraints. By numerically integrating the complete set of three coupled, nonlinear differential equations that describe the evolution of the inflaton field, radiation energy density, and background expansion, we obtain an exact description of the system's dynamics. Our results reveal that, while transition to radiation domination is suppressed in the weak regime, the strong dissipative regime leads to a smooth and natural transition to a hot, radiation-dominated Universe, thereby confirming graceful-exit within warm inflation in the quartic scenario. The reheating temperature is extracted directly from the nonlinear evolution of warm inflation, yielding a temperature of approximately 10^13 GeV at the end of inflation, which cools to about 10^12 GeV near radiation-inflaton equality, whence the Universe transitions into a radiation-dominated era.

Figures (13)

• Figure 1: Tensor-to-scalar ratio $r$ versus scalar spectral index $n_s$ in the weak dissipative regime for $a=9.4421\times 10^{-5}$. The straight line represents equation \ref{['comb1']}.
• Figure 2: Tensor-to-scalar ratio $r$ versus scalar spectral index $n_s$ in the strong dissipative regime for $a=4\times 10^{-2}$. The straight line represents equation \ref{['comb2']}.
• Figure 3: Tensor-to-scalar ratio $r$ versus scalar spectral index $n_s$ in the strong dissipative regime for $a=6\times 10^{-2}$. The straight line represents equation \ref{['comb2']}.
• Figure 4: Tensor-to-scalar ratio $r$ versus scalar spectral index $n_s$ in the strong dissipative regime for $a=8\times 10^{-2}$. The straight line represents equation \ref{['comb2']}.
• Figure 5: Tensor-to-scalar ratio $r$ versus scalar spectral index $n_s$ in the strong dissipative regime for $a=10\times 10^{-2}$. The straight line represents equation \ref{['comb2']}.