  The retarded gravitation produced by the matter and energy content of the
observable universe is formulated and shown how this cosmological gravity gives
rise to inertial forces in accelerated frames of reference. The model is
developed for spatially flat Friedman-Robertson-Walker (FRW) universes. The
retarded potential of cosmological gravity is determined first in fundamental
frames of reference, in Einstein-de Sitter (ES)and in LambdaCDM models. Despite
the expansion, the observable universe gives rise to a static, retarded
gravitational potential equal to c2 in ES universe, while gravity is weakening
during the expansion in LambdaCDM model.
  In the locally Minkowski spacetime occurring in a small domain of the
universe, a covariant Lagrangian of a test body moving in the cosmological
gravitational field is derived. Inertial forces are determined from a test
body's Euler-Lagrange equation, in Newtonian approximation. The model
calculation indicates, that the inertial forces meet exactly the ones observed
in ES universe and Mach's principle holds there. In the present-day standard,
LambdaCDM model inertial forces are weaker by 10 % than expected.
