Hybrid Inflation in Supergravity

For the last 15 years cosmologists believe that something like inflation is necessary in order to construct an internally consistent cosmological theory. For more than 20 years the best hopes for the theory of all fundamental interactions are related to supersymmetry. Unfortunately it is not that simple to combine these two ideas. The main problem is that the effective potential for the inflaton field σ in supergravity typically is too curved, growing as exp Cσ 2 M2 at large values of the inflaton field σ. HereM = 2.4×10 GeV is the stringy Planck mass. The typical value of the parameter C is O(1), which makes inflation impossible because the inflaton mass in this theory becomes of the order of the Hubble constant. Typical shape of the scalar field potential in superstring theory is exp Cσ M , which prevents inflation for σ > M . There are some cases where successful inflationary scenario can be developed despite these problems. Perhaps the easiest way to find a consistent inflationary model in supersymmetric theories is based on the hybrid inflation scenario [1]. In particular, recently a very interesting class of hybrid inflation models have been proposed based on the use of the D-term in the effective potential, which does not contain the exponentially growing factors [2]. However, in this paper we will concentrate on the model with the simplest choice of the superpotential which leads to hybrid inflation [3]