Vacuum stress tensor of spinor fields in de Sitter space

Abstract

We study the regularized vacuum stress tensor of spinor fields in de Sitter space and its possible contribution to the cosmological constant. Using adiabatic regularization, we show that the regularized stress tensor is maximally symmetric. It vanishes for the massless field, while for the massive field the vacuum energy density remains negative. The spinor vacuum therefore cannot by itself account for the observed positive cosmological constant, although it may contribute to the total vacuum energy. We revisit the adiabatic expansion of the spinor mode functions and find that several arbitrary functions in the WKB expansion cannot be fixed by the conditions given in the literature. However, their dependence cancels in the adiabatic power spectrum and spectral stress tensor, so that the physical quantities are uniquely determined. We further show that, in a general flat Robertson-Walker spacetime, the 2nd order adiabatic regularization is sufficient to remove all ultraviolet divergences in both quantities. Using point-splitting regularization, we derive the analytic correlation functions for both massless and massive spinor fields in de Sitter space that are valid at all scales, together with the adiabatic correlation functions. The regularized stress tensor obtained analytically in coordinate space agrees with those obtained from numerical integration of the adiabatically regularized spectra. The 2nd order regularized correlation function and stress tensor of the massive field reduce smoothly to those of the massless field in the massless limit, whereas the 4th order regularized results lack this property.

30 pages, 11 figures