One-loop effective action on rotational spacetime: ζ-Function regularization and Schwinger perturbative expansion

The ζ-function regularization method is used to evaluate the renormalized effective action for massless conformally coupling scalar fields propagating in a closed Friedmann spacetime perturbed by a small rotation. To the second order of the rotational parameter in the model spacetime the analytic form of the effective action is obtained with the help of the Schwinger perturbation formula. After investigating the time evolution of the rotational parameter we find that the quantum field effect can produce an effect which damps the cosmological rotation in the early universe.