From WMAP to Planck: Exact reconstruction of 4- and 5-dimensional inflationary potential from high precision CMB measurements

TL;DR

This paper develops an exact method to reconstruct inflationary potentials in 4-D and 5-D models from high-precision CMB data, avoiding slow-roll assumptions and analyzing uncertainties in reheating temperature.

Contribution

It introduces a general, assumption-minimal reconstruction approach for inflationary potentials using Hamilton-Jacobi formalism applicable to both 4-D and 5-D models.

Findings

Exact reconstruction of inflationary potentials without slow-roll approximation.

Analysis of the impact of reheating temperature uncertainties.

Evaluation of degeneracies in inflationary consistency relations.

Abstract

We make a more general determination of the inflationary observables in the standard 4-D and 5-D single-field inflationary scenarios, by the exact reconstruction of the dynamics of the inflation potential during the observable inflation with minimal number of assumptions: the computation does not assume the slow-roll approximation and is valid in all regimes if the field is monotonically rolling down its potential. Making use of the {\em Hamilton-Jacobi} formalism developed for the 5-D single-field inflation model,we compute the scale dependence of the amplitudes of the scalarand tensor perturbations by integrating the exact mode equation. We analyze the implications of the theoretical uncertainty in the determination of the reheating temperature after inflation on the observable predictions of inflation and evaluate its impact on the degeneracy of the standard inflation consistency relation.