Role of Heisenberg’s Uncertainty Principle in Dynamical Reheating of the Primordial Universe

In this work, we present a novel approach for studying the inflationary and reheating stages of the early universe by incorporating a quantum-mechanical constraint on radiation production, derived from the Heisenberg uncertainty principle. This constraint provides a fundamental upper bound on the rate at which radiation energy density can be generated, offering a novel framework for examining the efficiency and dynamics of energy transfer from the inflaton field to radiation. With this setup, we formulate a system of coupled, nonlinear differential equations that govern the depletion of inflaton energy, the growth of radiation, and the dynamics of cosmic expansion, ensuring consistency with exact energy conservation and accounting for backreaction from radiation production. Solving this nonlinear system numerically with initial conditions that satisfy the slow-roll criteria for 60 e-folds of inflation, we find that radiation production begins even during the inflationary phase and increases significantly afterwards. The reheating process is found to satisfy the Kofman-Yi criterion for successful reheating, with nearly all inflaton energy converted into radiation, reaching a peak radiation energy density, corresponding to a reheating temperature of \(T_r=2.38\times 10^{13}\) GeV. The evolution culminates in a dynamically smooth transition, a graceful exit, from inflation to a hot radiation-dominated Universe. Although we employ the quadratic potential to illustrate the significance of the approach, the methodology is generally applicable and can be adapted to observationally favored inflationary models.