On the slow roll expansion of one-field cosmological models

TL;DR

This paper analyzes the slow roll expansion in single-field cosmological models using Hamilton-Jacobi formalism, providing a recursive method to construct higher order terms and exploring related potentials and symmetries.

Contribution

It introduces an explicit recursion procedure for higher order slow roll expansion terms via Hamilton-Jacobi formalism in cosmology.

Findings

Slow roll expansion coincides with Laurent expansion of Hamilton-Jacobi function.

Recursion method for constructing higher order terms.

Analysis of effective potential and universal symmetry group.

Abstract

We study the infrared scale expansion of single field cosmological models using the Hamilton-Jacobi formalism, showing that its specialization at unit scale parameter recovers the slow roll expansion. In particular, we show that the latter coincides with a Laurent expansion of the Hamilton-Jacobi function in powers of the Planck mass, whose terms are controlled by certain recursively-defined polynomials. This allows us to give an explicit recursion procedure for constructing all higher order terms of the slow roll expansion. We also discuss the corresponding effective potential and the action of the universal similarity group.