O(N)quantum fields in curved spacetime

For the O$\mathrm{}\left(N\right)\mathrm{}$ field theory with $\lambda {\Phi }^4$ self-coupling, we construct the two-particle-irreducible (2PI) closed-time-path (CTP) effective action in a general curved spacetime. From this we derive a set of coupled equations for the mean field and its variance. They are useful for studying the nonperturbative, nonequilibrium dynamics of a quantum field when full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field, are required. Applications to phase transitions in the early Universe such as at the Planck scale or in the reheating phase of chaotic inflation are under investigation.