Hyperbolic Inflation in the Light of Planck 2015 data

TL;DR

This paper explores hyperbolic scalar field potentials for inflation, deriving analytical expressions for key parameters, and tests their compatibility with Planck 2015 data to assess their viability in early universe cosmology.

Contribution

It introduces an analytical framework for hyperbolic scalar field inflation models and compares their predictions with Planck 2015 observations.

Findings

Analytical expressions for slow-roll parameters derived.

Model predictions are consistent with Planck 2015 data.

Hyperbolic inflation models are viable candidates for early universe inflation.

Abstract

Rubano and Barrow have discussed the emergence of a dark energy, with late-time cosmic acceleration arising from a self-interacting homogeneous scalar field with a potential of hyperbolic power type. Here, we study the evolution of this scalar field potential back in the inflationary era. Using the hyperbolic power potential in the framework of inflation, we find that the main slow-roll parameters, like the scalar spectral index, the running of the spectral index and the tensor-to-scalar fluctuation ratio can be computed analytically. Finally, in order to test the viability of this hyperbolic scalar field model at the early stages of the Universe, we compare the predictions of that model against the latest observational data, namely Planck 2015.