Adiabatic regularization with a Yukawa interaction

Abstract

We extend the adiabatic regularization method for an expanding universe to include the Yukawa interaction between quantized Dirac fermions and a homogeneous background scalar field. We give explicit expressions for the renormalized expectation values of the stress-energy tensor $⟨T_{\mu \nu }⟩$ and the bilinear $⟨\bar{\psi }\psi ⟩$ in a spatially flat FLRW spacetime. These are basic ingredients in the semiclassical field equations of fermionic matter in curved spacetime interacting with a background scalar field. The ultraviolet subtracting terms of the adiabatic regularization can be naturally interpreted as coming from appropriate counterterms of the background fields. We fix the required covariant counterterms. To test our approach we determine the contribution of the Yukawa interaction to the conformal anomaly in the massless limit and show its consistency with the heat kernel method using the effective action.

31 pages, 1 figure. Small change in title. Some points have been clarified. Added references. Corrected typos

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• Cosmological decay of Higgs-like scalars into a fermion channel
• R-summed form of adiabatic expansions in curved spacetime
• Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes
• Optomechanical Backreaction of Quantum Field Processes in Dynamical Casimir Effect
• Renormalization, running couplings and decoupling for the Yukawa model in curved spacetime
• Ultralight dark matter or dark radiation cosmologically produced from infrared dressing
• Induced energy-momentum tensor of Dirac field in 2D de Sitter QED
• Physical scale adiabatic regularization in cosmological spacetimes