On the slow roll expansion of one-field cosmological models

We study the infrared scale expansion of single field cosmological models using the HamiltonJacobi formalism, showing that its specialization at unit scale parameter recovers the roll expansion. In particular, we show that the latter coincides with a Laurent expansion the Hamilton-Jacobi function in powers of the Planck mass, whose terms are controlled certain recursively-defined polynomials. This allows us to give an explicit recursion procedure 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.