Helmoltz problem for the Riccati equation from an analogous Friedmann equation

Valerio Faraoni

doi:10.1140/epjc/s10052-021-09966-0

Helmoltz problem for the Riccati equation from an analogous Friedmann equation

Eur Phys J C Part Fields. 2022;82(1):13. doi: 10.1140/epjc/s10052-021-09966-0. Epub 2022 Jan 7.

Author

Valerio Faraoni¹

Affiliation

¹ Department of Physics and Astronomy, Bishop's University, 2600 College Street, Sherbrooke, QC J1M 1Z7 Canada.

Abstract

We report a solution of the inverse Lagrangian problem for the first order Riccati differential equation by means of an analogy with the Friedmann equation of a suitable Friedmann-Lemaître-Robertson-Walker universe in general relativity. This analogous universe has fine-tuned parameters and is unphysical, but it suggests a Lagrangian and a Hamiltonian for the Riccati equation and for the many physical systems described by it.