Reconstructing square-law k-inflation from Planck data

TL;DR

This paper investigates a square-law k-inflation model using the Hamilton-Jacobi approach, deriving key observables, constraining parameters with Planck data, and showing the model's compatibility with observations.

Contribution

It introduces a specific square-law k-inflation model with a power-law Hubble parameter and constrains it using Planck data, providing a new viable inflationary scenario.

Findings

Model aligns well with Planck observations

Derived explicit form of the inflationary potential

Computed key inflationary observables

Abstract

We explore a square-law k-inflation using the Hamilton-Jacobi approach. Focusing on scenarios where the Hubble parameter exhibits a power-law dependence on the k-field, our analysis encompasses the computations of crucial observables, such as the scalar power spectrum, the tensor-to-scalar ratio, and the scalar spectral index. We further constrain the model's parameters using Planck data and present a specific form of the potential. Our results demonstrate that the model aligns well with observational data.