  This is an example of application of Ziglin-Morales-Ramis algebraic studies
in Hamiltonian integrability, more specifically 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.
