Finite-temperature quantum field theory in curved spacetime: Quasilocal effective Lagrangians

We use momentum-space techniques and a quasilocal expansion to derive the imaginary-time thermal Green’s functions and the one-loop finite-temperature effective Lagrangians for λ${\phi }^4$ fields in curved spacetimes. These approximations are useful for treating quasiequilibrium conditions associated with gradual changes in the background fields and the background spacetimes. For problems in spacetimes with small curvature, we use a Riemann normal coordinate for the background metric, a derivative expansion for the background field, and a small-proper-time Schwinger-DeWitt expansion to derive the finite-temperature effective Lagrangians. For problems in homogeneous cosmology we consider conformally related fields and the Robertson-Walker universe as background to carry out finite-temperature perturbation calculations. We study a massless conformal λ${\phi }^4$ theory in a Bianchi type-I universe and derive the finite-temperature effective Lagrangian in orders of small anisotropy. The quasilocal method presented here is related to the adiabatic method in finite-temperature quantum field theory presented earlier in similar settings. These results are useful for the study of quantum thermal processes in the early Universe.