  We investigate the cosmological implications of a new class of modified
gravity, where the field equations generically include higher-order derivatives
of the matter fields, arising from the introduction of non-dynamical auxiliary
fields in the action. Imposing a flat, homogeneous and isotropic geometry we
extract the Friedmann equations, obtaining an effective dark-energy sector
containing higher derivatives of the matter energy density and pressure. For
the cases of dust, radiation, and stiff matter we analyze the cosmological
behavior, finding accelerating, de Sitter, and non-accelerating phases,
dominated by matter or dark energy. Additionally, the effective dark-energy
equation-of-state parameter can be quintessence-like,
cosmological-constant-like, or even phantom-like. The detailed study of these
scenarios may provide signatures that could distinguish them from other
candidates of modified gravity.
