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 adiabatic ($\Phi$) and isocurvature ($S_{(ij)}$ or $\delta \phi_{(ij)}$) perturbation variables in the general background with $K$ and $\Lambda$. We clarify the conditions for conserved adiabatic and isocurvature perturbations in the large-scale limit. Evolutions of curvature perturbations in many different gauge conditions are analysed extensively. In the ideal fluid system it is known that the isocurvature modes can seed the adiabatic mode in the large-scale limit whereas the isocurvature modes decouple from the adiabatic one. In the multiple field system, however, both modes are directly seeding each other even in the large-scale limit. In the multi-field system we present a general solution to the linear order in slow-roll parameters.