Hybrid Inflation in Supergravity with $(SU(1,1)/U(1)) ^{m}$ K$% \ddot{a}$hler Manifolds

Abstract

In the presence of fields without superpotential but with large vevs through D-terms the mass-squared of the inflaton in the context of supergravity hybrid inflation receives positive contributions which could cancel the possibly negative K$\ddot{a}$hler potential ones. The mechanism is demonstrated using K$\ddot{a}$hler potentials associated with products of $SU(1,1)/U(1)$ K$\ddot{a}$hler manifolds. In a particularly simple model of this type all supergravity corrections to the F-term potential turn out to be proportional to the inflaton mass allowing even for an essentially completely flat inflationary potential. The model also allows for a detectable gravitational wave contribution to the microwave background anisotropy. Its initial conditions are quite natural largely due to a built in mechanism for a first stage of ``chaotic'' D-term inflation.