Evidence and conditions for non-integrability in the Friedmann-Robertson-Walker Hamiltonian

Sergi Simon

Published 2013-09-11Version 1

This is an example of application of Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more speci?cally the result by Morales, Ramis and Sim\'o on higher-order variational equations, to the well-known Friedmann-Robertson-Walker cosmological model. A previous paper by the author formalises said variational systems in such a way allowing the simple expression of notable elements of the differential Galois group needed to study integrability. Using this formalisation and an alternative method already used by other authors, we find sufficient conditions whose fulfillment would entail very simple proofs of non-integrability -- both for the complete Hamiltonian, a goal already achieved by other means by Coelho et al, and for a special open case attracting recent attention.