Cosmology with higher-derivative matter fields

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.