Supergravity modification of D-term hybrid inflation:: Solving the cosmic string and spectral index problems via a right-handed sneutrino

Supergravity corrections due to the energy density of a right-handed sneutrino can generate a negative mass squared for the inflaton, flattening the inflaton potential and reducing the spectral index and inflaton energy density. For the case of D-term hybrid inflation, we show that the spectral index can be lowered from the conventional value n=0.98 to a value within the range favored by the latest WMAP analysis, n=0.951(-0.019)(+0.015). The modified energy density is consistent with nonobservation of cosmic strings in the CMB if n < 0.946. The WMAP lower bound on the spectral index implies that the D-term cosmic string contribution may be very close present CMB limits, contributing at least 5% to the CMB multipoles.