# Reconstruction of initial Asymptotic-de Sitter mode in light of the Planck data

## TL;DR

This paper reconstructs an initial asymptotic de Sitter mode for inflation using Planck data, revealing deviations from pure de Sitter and Bunch-Davies modes, and constrains related parameters with observational data.

## Contribution

It introduces a parametrized asymptotic de Sitter mode for primordial spectrum reconstruction and constrains it using Planck data, showing deviations from standard models.

## Key findings

- Deviation from pure de Sitter/Bunch-Davies mode (~0.03-0.04)
- Scalar perturbation amplitude consistent with Planck 2015 data
- Upper limits on tensor-to-scalar ratio: r_{0.05}<0.0272, r_{0.002}<0.0242

## Abstract

The recently relased \emph{Planck} data, emphasize that the background geometry of 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 reconstruction 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 our parametrized asymptotic initial mode shows some deviation from pure de Sitter or Bunch-Davies mode. Based on \emph{Planck 2015} data release the amplitude of scalar perturbations in $ 68 \%$ confidence level is $10^{9} A_s =2.77^{+0.32}_{-0.35}$ and deviation from Bunch-Davies mode is $\sim 0.03-0.04$. In this parametrization, the CMB power spectrum of our model shows more red-tilt in comparison with $\Lambda \rm{CDM}$ model. Furthermore, we found upper limit for tensor-to-scalar ratio with different pivot scales $r_{0.05}< 0.0272$ and $ r_{0.002}< 0.0242$.

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Source: https://tomesphere.com/paper/1702.08790