jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pThe generic scale-invariant theory of an axion and a dilaton coupled to gravity in jats:italicd</jats:italic>-dimensions is generalized to a ‘universal’ one-axion model with two dilatons that reproduces itself under consistent dimensional-reduction/truncation. Flat FLRW cosmologies are shown to correspond to trajectories of a three-dimensional autonomous dynamical system, which we analyse with a focus on accelerated cosmic expansion, deriving the precise swampland bounds that exclude eternal acceleration. We also show that for two sets of values of its three independent parameters, the model is a consistent truncation of maximal ‘massive’ supergravity theories arising from string/M-theory; for these maximal-supergravity parameter values the FLRW cosmologies include some with a transient de Sitter-like phase, but not the recurring de Sitter-like phase or eternal cosmic acceleration that is possible for other parameter values.</jats:p>