Abstract
Finite temperature corrections to the effective potential and the energy-momentum tensor of a scalar field are computed in a perturbed Minkoswki space-time. We consider the explicit mode decomposition of the field in the perturbed geometry and obtain analytical expressions in the non-relativistic and ultra-relativistic limits to first order in scalar metric perturbations. In the static case, our results are in agreement with previous calculations based on the Schwinger-De Witt expansion which indicate that thermal effects in a curved space-time can be encoded in the local Tolman temperature at leading order in perturbations and in the adiabatic expansion. We also study the shift of the effective potential minima produced by thermal corrections in the presence of static gravitational fields. Finally we discuss the dependence on the initial conditions set for the mode solutions.
Highlights
Finite-temperature corrections to the effective potential in quantum field theory play a fundamental role in the description of phase transitions in the early Universe
Our results are in agreement with previous calculations based on the Schwinger-DeWitt expansion which indicate that thermal effects in a curved spacetime can be encoded in the local Tolman temperature at leading order in perturbations and in the adiabatic expansion
We study the shift of the effective potential minima produced by thermal corrections in the presence of static gravitational fields
Summary
An alternative approach to the adiabatic expansion for thermal field theory in general curved spacetime is the socalled Schwinger-DeWitt [7,8] expansion of the effective action. [12] to isolate the divergences, applying techniques developed to deal with nonrational integrands In this case, the renormalized effective potential, being explicitly covariant, did not contain contributions from the inhomogeneous gravitational fields at the leading order in metric perturbation and in the adiabatic expansion in both static and cosmological spacetimes. We find that local gravitational effects can be taken into account through the Tolman temperature [13] This is in accordance with computations of the energy-momentum tensor of a scalar field at finite temperature in a static spacetime using the Schwinger-DeWitt approach, [14,15].
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