ABSTRACT
This chapter discusses inflation model-building. It presents some of the main slow-roll inflation models; some of the most successful ones. Hybrid inflation was originally introduced by Andrei D. Linde in 1994 to overcome the problem of super-Planckian expectation values of the inflaton field in monomial chaotic inflation. The mechanism of warm inflation has been considered with a multitude of inflation models, mostly of the archetype kind, like chaotic, hilltop or hybrid inflation. Many variants of such models exist, going by names such as supernatural inflation or mutated hybrid inflation. Depending of the order of the pole, when we turn to the canonical field we may arrive at Starobinsky inflation, T-model inflation but also hilltop inflation or inverted hilltop inflation and so on. Higgs inflation has the unique property of leading to fully determined reheating, because the decay rates of the Higgs field to standard model particles are known.
