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 K{ä}hler potential ones. The mechanism is demonstrated using K{ä}hler potentials associated with products of $SU(1,1)/U(1)$ K{ä}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 for an essentially completely flat inflationary potential above the Planck scale. The model also allows for a detectable gravitational wave contribution to the microwave background anisotropy.