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 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 that are valid in Einstein’s gravity. This unified and simple treatment is possible due to our proper choice of the gauges, or equivalently gauge invariant combinations. © 1996 The American Physical Society.

• Received 9 August 1995

DOI:https://doi.org/10.1103/PhysRevD.53.762