A Brachistochrone Approach to Reconstruct the Inflaton Potential

TL;DR

This paper introduces a novel method to reconstruct the inflaton potential using a brachistochrone-inspired approach that models the Hubble parameter without relying on the slow-roll approximation, enabling more flexible inflationary prior implementation.

Contribution

It presents a new framework for inflationary potential reconstruction based on the brachistochrone problem, extending beyond traditional slow-roll assumptions.

Findings

The method employs an exponential form for H(φ) capturing inflationary dynamics.

It provides a unique solution to the brachistochrone problem in the context of inflation.

The approach allows for arbitrary order inclusion of inflationary observables.

Abstract

We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(\phi)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(\phi)$ has the unique property that it is the solution to the brachistochrone problem for inflation.