Gravitational Zero Point Energy and the Induced Cosmological Constant

Details Gravitational Zero Point Energy and the Induced Cosmological Constant Gravitational Zero Point Energy and the Induced Cosmological Constant

2010-07-29

arxiv.org/abs/1007.5227v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX 10 Pages. Submitted to the volume "Cosmology, Quantum Vacuum, and Zeta Functions", in honour of Professor Emilio Elizald

Scientific paper

We discuss how to extract information about the cosmological constant from the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville problem in a generic spherically symmetric background. The equation is approximated to one loop with the help of a variational approach with Gaussian trial wave functionals. A canonical decomposition of modes is used to separate transverse-traceless tensors (graviton) from ghosts and scalar. We show that no ghosts appear in the final evaluation of the cosmological constant. A zeta function regularization and a ultra violet cutoff are used to handle with divergences. A renormalization procedure is introduced to remove the infinities. We compare the result with the one obtained in the context of noncommutative geometries

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