Cosmological perturbations with multiple fluids and fields

We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (Φ or φχ) and isocurvature (S(ij) or δφ(ij)) perturbation variables in the general background with K and Λ. We clarify the conditions for conserved curvature and isocurvature perturbations in the large-scale limit. Evolutions of curvature perturbations in many different gauge conditions are analysed extensively. In the multi-field system we present a general solution to the linear order in slow-roll parameters