We reformulate the dynamics of homogeneous cosmologies with a scalar field matter source with an arbitrary self-
interaction potential in the language of jet bundles and extensions of vector fields. In this framework, the Bianchi—
scalar field equations become subsets of the second Bianchi jet bundle, J2 , and every Bianchi cosmology is naturally
extended to live on a variety of J2 . We are interested in the existence and behaviour of extensions of arbitrary
Bianchi-Lie and variational vector fields acting on the Bianchi variety and accordingly we classify all such vector
fields corresponding to both Bianchi classes A and B. We give examples of functions defined on Bianchi jet bundles
which are constant along some Bianchi models (first integrals) and use these to find particular solutions in the
Bianchi total space. We discuss how our approach could be used to shed new light to questions like isotropization
and the nature of singularities of homogeneous cosmologies by examining the behaviour of the variational vector
fields and also give rise to interesting questions about the ‘evolution’ and nature of the cosmological symmetries
themselves.
