Reheating after inflation

The theory of reheating of the Universe after inflation is developed. We have found that typically at the first stage of reheating the classical inflation field φ rapidly decays into φ particles or into other bosons due to a broad parametric resonance. Then these bosons decay into other particles, which eventually become thermalized. Complete reheating is possible only in those theories where a single particle φ can decay into other particles. This imposes strong constraints on the structure of inflationary models, and implies that the inflation field can be a dark matter candidate.