Scalar and tensor power spectra in a universe with positive curvature index and maximally symmetric spatial section

Abstract

Abstract Recently, some departures from the Λ CDM model have been reported by WMAP and Planck satellites such as suppression of the lowest CMB multipoles, and the hemispherical asymmetry in CMB anisotropy plan. It motivates us to consider models with nonzero curvature index and study the imprints of curvature and topology on the observed anomalies. So in this article we study the positively curved inflationary paradigm. For this purpose, first, we derive the power spectra of comoving curvature perturbation and primordial gravitational waves in the FLRW universes with K = + 1 and maximally symmetry spatial sections according to the slowly rolling inflationary scenario. Our study includes two spherical and elliptical models with S 3 and R P 3 as the spatial topology respectively. It can be shown that the curvature spectral index in this model automatically has a small negative running parameter which is compatible with observational measurements. We also investigate the relative amplitude of the scalar and tensor perturbations. It will be clear that the tensor–scalar ratio for both models are equal and depends on the wavelength of the perturbations severely. Furthermore, the discrepancy between BICEP2 results and slow-rolling inflationary model in spatially flat background may be reduced although it does not seem statistically significant.