Asymptotic-de sitter inflation in the light of the planck data**Supported by Islamic Azad University- Rasht Branch, Rasht, Iran

Abstract

Planck 2015 data, emphasize that the background geometry during inflation is not pure de Sitter, but from the slow variation of Hubble parameter during the inflationary era, it can be quasi-de Sitter. This motivates us to consider an Asymptotic-de Sitter mode function for reconstructing of initial mode and primordial power spectrum of curvature perturbation. Using Markov Chain Monte Carlo (MCMC) method together with applying recent observational constraints from the Cosmic Microwave Background (CMB) data for the parameterized asymptotic initial mode in term of c, show some deviation from Bunch-Davies mode (c = 1). Based on Planck 2015 data release the amplitude of scalar perturbations in 68% confidence level is and deviation from Bunch-Davies mode is ∼ 0.05, i.e. c ∼ 1.05. In this parametrization, the CMB power spectrum of our model shows more red-tilt in comparison with ΛCDM model. Furthermore, we found upper limits for tensor-to-scaler ratio with different pivot scales.