Slow-roll inflationary scenario in the maximally extended background

During the inflationary epoch, the geometry of the universe may be described by a quasi-de Sitter space. On the other hand, the maximally extended de Sitter metric in the comoving coordinates accords with a special FLRW model with positive spatial curvature; therefore, the focus of the present paper is on the positively curved inflationary paradigm, for which we first of all derive the power spectra of comoving curvature perturbation and primordial gravitational waves in a positively curved FLRW universe according to the slowly rolling inflationary scenario. It can be shown that the curvature spectral index in this model automatically has a small negative running parameter, compatible with observational measurements. Afterwards, by taking into account the curvature factor, it investigates the relative amplitude of the scalar and tensor perturbations, clarifying that the tensor–scalar ratio for this model, against the spatially flat one, directly depends on the wavelength of the perturbative modes.