Abstract
We review the adiabatic renormalization method for spin-1/2 fields in FLRW spacetimes, emphasizing its similarities and differences with the scalar case. With it, we obtain a generic expression for the renormalized expectation value of the stress-energy tensor and analyze its properties. We particularize this result to de Sitter and radiation-dominated universes, recovering in the second case the equations of cold matter for late times.
Highlights
The renormalization of quantum fields in curved spacetime is an extensively studied issue [1, 2]
The key difference between both cases is that in the first one, the adiabatic expansion that identifies the divergent terms is of WKB type, while in the second one it is not
In order to check the validity of our approach, we renormalized adiabatically the trace and chiral anomalies and checked that our results were coincident with those obtained with other renormalization procedures
Summary
The renormalization of quantum fields in curved spacetime is an extensively studied issue [1, 2]. One of the most useful for FLRW metrics is adiabatic regularization In this method, the divergent terms are identified and subtracted through an expansion in momenta of the field modes defining the quantum state. The divergent terms are identified and subtracted through an expansion in momenta of the field modes defining the quantum state By dimensionality, this is equivalent to an expansion in derivatives of the scale factor, the adiabatic denomination. Adiabatic expansion The adiabatic regularization method is based on an expansion in momenta of the field modes (hIk and hIkI for spin-1/2 fields, and fk for scalars) This construction allows afterwards to identify and subtract the divergent terms from the original quantity.
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