Supersymmetric Hybrid Inflation

The non-supersymmetric and supersymmetric versions of hybrid inflation are summarized. In the latter, the necessary inclination along the inflationary trajectory is provided by radiative corrections. Supersymmetric hybrid inflation (with its extensions) is an extremely ‘natural’ inflationary scenario. The reasons are that it does not require ‘tiny’ parameters, its superpotential has the most general form allowed by the symmetries, and it can be protected against radiative or supergravity corrections. Concrete supersymmetric grand unified theories, which lead to hybrid inflation, solve the μ problem via a Peccei-Quinn symmetry and generate seesaw masses for the light neutrinos, can be constructed. As an example, we present a theory with unified gauge group SU(3)C × SU(2)L × SU(2)R × U(1)B-L. The ‘reheating’ which follows hybrid inflation is studied. It is shown that the gravitino constraint on the ‘reheat’ temperature can be ‘naturally’ satisfied. Also, the observed baryon asymmetry of the universe can be generated via a primordial leptogenesis consistent with the requirements from solar and atmospheric neutrino oscillations. Extensions of the standard supersymmetric hybrid inflationary scenario, which are still consistent with all these requirements but can also avoid the cosmological disaster from the possible copious monopole production at the abrupt termination of standard hybrid inflation, are constructed. They rely on utilizing the leading non-renormalizable correction to the standard hybrid inflationary superpotential and are necessary for higher unified gauge groups such as SU(4)C × SU(2)L × SU(2)R which predict the existence of monopoles. In one extension, which we call shifted hybrid inflation, the relevant part of inflation takes place along a ‘shifted’ classically flat direction on which the unified gauge symmetry is already broken. In the other extension, called smooth hybrid inflation, the trilinear term of the standard hybrid inflationary superpotential is removed by a discrete symmetry. The inflationary path then possesses a classical inclination and the termination of inflation is smooth.