  We discuss a field-theoretical approach based on variational principle to
derive the field and hydrodynamic equations of motion of baryonic matter
governed by cosmological perturbations of dark matter and dark energy. The
action depends on the gravitational and matter Lagrangian. The gravitational
Lagrangian depends on the metric tensor and its first and second derivatives.
The matter Lagrangian includes dark matter, dark energy and the ordinary
baryonic matter. The total Lagrangian is expanded in an asymptotic Taylor
series around the background manifold defined as a solution of Einstein's
equations in the form of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric
tensor. The small parameter of the decomposition is the magnitude of the metric
tensor perturbation. Each term of the series expansion is gauge-invariant and
all of them together form a basis for the successive post-Friedmannian
approximations. The approximation scheme is covariant and the asymptotic nature
of the Lagrangian decomposition does not require the post-Friedmannian
perturbations to be small though computationally it works the most effectively
when the perturbed metric is close enough to the background FLRW metric. The
temporal evolution of the background metric is governed by dark matter and dark
energy and we associate the large scale inhomogeneities in these two components
as those generated by the primordial cosmological perturbations. The small
scale inhomogeneities are generated by the condensations of baryonic matter
considered as the bare perturbations. We explicitly work out the covariant
field equations of the successive post-Friedmannian approximations of
Einstein's equations and derive equations of motion of large and small scale
inhomogeneities of dark matter and dark energy. We apply these equations to
derive the post-Friedmannian equations of motion of the baryonic matter.
