  The problem of explaining both inflationary and dark matter physics in the
framework of a minimal extension of the Standard Model was investigated. To
this end, the Standard Model completed by a real scalar singlet playing a role
of the dark matter candidate has been considered. We assumed both the dark
matter field and the Higgs doublet to be nonminimally coupled to gravity. Using
quantum field theory in curved spacetime we derived an effective action for the
inflationary period and analyzed its consequences. In this approach, after
integrating out both dark matter and Standard Model sectors we obtained the
effective action expressed purely in terms of the gravitational field. We paid
special attention to determination, by explicit calculations, of the form of
coefficients controlling the higher-order in curvature gravitational terms.
Their connection to the Standard Model coupling constants has been discussed.
