Hybrid inflation in supergravity with (SU(1,1)/U(1))m Kähler manifolds

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 Kähler potential ones. The mechanism is demonstrated using Kähler potentials associated with products of SU(1,1)/U(1) Kähler 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.