We consider the instability of the Friedmann world model to second order in perturbations. We present the perturbed set of equations up to second order in the Friedmann background world model with a general spatial curvature and cosmological constant. We consider systems with completely general imperfect fluids, minimally coupled scalar fields, an electromagnetic field, and generalized gravity theories. We also present the case of null geodesic equations, and one based on the relativistic Boltzmann equation. In due time, a decomposition is made for scalar-, vector-, and tensor-type perturbations which couple with each other to second order. A gauge issue is resolved to each order. The basic equations are presented without imposing any gauge condition, and thus in a gauge-ready form so that we can take full advantage of having gauge freedom in analyzing the problems. As an application we show that to second order in perturbation the relativistic pressureless ideal fluid of the scalar type reproduces exactly the known Newtonian result. As another application we rederive the large-scale conserved quantities ͑of the pure scalar and tensor perturbations͒ to second order, first shown by Salopek and Bond, now from the exact equations. Several other applications are shown as well.

We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these variety of gravity theories are presented in unified forms. These apply both to the scalar-and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein's gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflations and its consequent power spectra are derived in unified forms which include wide range of inflationary scenarios based on Einstein's gravity and others.

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We analyze the cosmological perturbations valid in a broad class of generalized gravity theories in a unified manner. A complete set of perturbation equations is derived in gauge-ready forms. We present general asymptotic solutions for several different choices of the gauge conditions in unified forms. As in the case of Einstein's gravity, the uniform-curvature gauge is particularly simple for treating the scalar-type perturbations in generalized gravity theories involving the scalar field and the scalar curvature. Remarkably, considering the growing mode in the uniform-curvature gauge, the same solutions derived in Einstein's gravity remain valid in a broad class of generalized gravity theories. ͓S0556-2821͑96͒06012-2͔PACS number͑s͒: 04.50.ϩh, 04.62.ϩv, 98.80.Hw

The author presents a simple way of deriving cosmological perturbation equations in generalised gravity theories which accounts for metric perturbations in a gauge-invariant way. The author uses an imperfect fluid formulation of the perturbation equations developed in Einstein gravity and absorb all new contributions as effective fluid quantities. The author applies this approach to the f( phi , R)- omega ( phi ) phi ,c phi c Lagrangian which includes most of the gravity theories employing a scalar field and scalar curvature. The relation between the proposed method and the conformal transformation method is discussed. Background and perturbation equations are displayed for specific gravity theories which can be recovered as special cases from the above general Lagrangian.