Effective Action for Cosmological Scalar Fields at Finite Temperature
  Scalar fields appear in many theories beyond the Standard Model of particle
physics. In the early universe, they are exposed to extreme conditions,
including high temperature and rapid cosmic expansion. Understanding their
behavior in this environment is crucial to understand the implications for
cosmology. We calculate the finite temperature effective action for the field
expectation value in two particularly important cases, for damped oscillations
near the ground state and for scalar fields with a flat potential. We find that
the behavior in both cases can in good approximation be described by a complex
valued effective potential that yields Markovian equations of motion. Near the
potential minimum, we recover the solution to the well-known Langevin equation.
For large field values we find a very different behavior, and our result for
the damping coefficient differs from the expressions frequently used in the
literature. We illustrate our results in a simple scalar model, for which we
give analytic approximations for the effective potential and damping
coefficient. We also provide various expressions for loop integrals at finite
temperature that are useful for future calculations in other models.
