Open hybrid inflation

We propose an open hybrid inflation scenario that produces an open universe with a ''tilted'' n>1 spectrum of metric perturbations. The model contains a symmetry-breaking field that tunnels to its true vacuum, producing a single bubble inside which hybrid inflation drives the universe to almost flatness. In order to obtain density perturbations with n>1 we analyze a recently proposed new version of hybrid inflation scenario called tilted hybrid inflation. In this scenario, unlike in the previously known versions of hybrid inflation, a considerable tilt of the spectrum can be obtained without fine tuning. The stage of inflation in this model is rather short which allows us to obtain an inflationary universe with Omega<1 in a more natural way. We study the separate contribution of scalar perturbations coming from the continuum subcurvature modes, the discrete supercurvature mode, and the bubble wall mode to the angular power spectrum of temperature fluctuations in open inflation. We derive bounds on the parameters of the model so that the predicted spectrum is compatible with the observed anisotropy of the microwave background.