Gravitational Zero Point Energy and the Induced Cosmological Constant

Abstract

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

LaTeX 10 Pages. Submitted to the volume "Cosmology, Quantum Vacuum, and Zeta Functions", in honour of Professor Emilio Elizalde on the occasion of his 60th birthday

References in corpus (4)

• Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
• The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint
• A noncommutative approach to the cosmological constant problem
• One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly