Tilted non-spatially-flat inflation

We construct non-linear inflaton potential energy densities that describe not-necessarily very-slowly-rolling closed and open inflation models, and compute tilted primordial spatial inhomogeneity power spectra that follow from quantum mechanical fluctuations during inflation in these models. Earlier non-flat inflation model power spectra computations assumed an inflaton potential energy density with a linear slope that resulted in very-slow-roll during inflation and untilted power spectra. These new tilted power spectra differ from those that have previously been used to study cosmological data in non-flat cosmological models.