4.4 Article

Effective action for cosmological scalar fields at finite temperature

Journal

JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 8, Pages -

Publisher

SPRINGER
DOI: 10.1007/JHEP08(2015)059

Keywords

Cosmology of Theories beyond the SM; Thermal Field Theory; Quantum Dissipative Systems; Effective field theories

Funding

  1. Jiangsu Ministry of Science and Technology [BK20131264]
  2. Chinese Ministry of Education
  3. Priority Academic Program Development for Jiangsu Higher Education Institutions (PAPD)
  4. Gottfried Wilhelm Leibniz program of the Deutsche Forschungsgemeinschaft (DFG)
  5. DFG cluster of excellence Origin and Structure of the Universe

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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.

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