  In this paper we address the issue of exploring some cosmological scenarios
in modified Einstein gravity through non-dynamical (auxiliary) fields. We found
that all scenarios are controlled by a specific parameter associated with an
auxiliary field. We explore the emergence of inflationary, radiation, matter
and dark energy dominated regimes. Furthermore, an interesting possibility such
as the emergence of a self-tuning mechanism to the cosmological constant
problem in the radiation dominated era is also discussed.
