The paper by Lev Kofman, Andrei Linde, and Alexei A. Starobinsky discusses the theory of reheating in the universe after inflation. They find that the process typically consists of three stages: pre-heating, particle decay, and thermalization. In the pre-heating stage, the classical inflaton field $\phi$ rapidly decays into $\phi$-particles or other bosons due to a broad parametric resonance, leading to an explosive decay. This stage is followed by the decay of these particles into other particles, which eventually thermalize. Complete reheating is possible only in theories where a single $\phi$ particle can decay into other particles, imposing constraints on inflationary models and suggesting that the inflaton field could be a dark matter candidate. The authors use a simple chaotic inflation scenario to illustrate these processes and provide detailed mathematical derivations for various inflationary models, including those with spontaneous symmetry breaking. They also discuss the implications of these findings for cosmological scenarios, such as the suppression of primordial black holes.The paper by Lev Kofman, Andrei Linde, and Alexei A. Starobinsky discusses the theory of reheating in the universe after inflation. They find that the process typically consists of three stages: pre-heating, particle decay, and thermalization. In the pre-heating stage, the classical inflaton field $\phi$ rapidly decays into $\phi$-particles or other bosons due to a broad parametric resonance, leading to an explosive decay. This stage is followed by the decay of these particles into other particles, which eventually thermalize. Complete reheating is possible only in theories where a single $\phi$ particle can decay into other particles, imposing constraints on inflationary models and suggesting that the inflaton field could be a dark matter candidate. The authors use a simple chaotic inflation scenario to illustrate these processes and provide detailed mathematical derivations for various inflationary models, including those with spontaneous symmetry breaking. They also discuss the implications of these findings for cosmological scenarios, such as the suppression of primordial black holes.