In a class of generalized Einstein's gravity theories we derive the equations
and general asymptotic solutions describing the evolution of the perturbed
universe in unified forms. Our gravity theory considers general couplings
between the scalar field and the scalar curvature in the Lagrangian, thus
includes broad classes of generalized gravity theories resulting from recent
attempts for the unification. We analyze both the scalar-type mode and the
gravitational wave in analogous ways. For both modes the large scale evolutions
are characterized by the same conserved quantities which are valid in the
Einstein's gravity. This unified and simple treatment is possible due to our
proper choice of the gauges, or equivalently gauge invariant combinations.Comment: 4 pages, revtex, no figure