  We study how inhomogeneities of the cosmological fluid fields backreact on
the homogeneous part of energy density and how they modify the Friedmann
equations. In general, backreaction requires to go beyond the pressureless
ideal fluid approximation, and this can lead to a reduced growth of
cosmological large scale structure. Since observational evidence favours
evolution close to the standard growing mode in the linear regime, we focus on
two-component fluids in which the non-ideal fluid is gravitationally coupled to
cold dark matter and in which a standard growing mode persists. This is
realized, e.g. for a baryonic fluid coupled to cold dark matter. We calculate
the backreaction for this case and for a wide range of other two-fluid models.
Here the effect is either suppressed because the non-ideal matter properties
are numerically too small, or because they lead to a too stringent UV cut-off
of the integral over the power spectrum that determines backreaction. We
discuss then matter field backreaction from a broader perspective and
generalize the formalism such that also far-from-equilibrium scenarios relevant
to late cosmological times and non-linear scales can be addressed in the
future.
