The Cosmological constant and the Wheeler-DeWitt Equation
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. 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 is used to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. A brief discussion on the extension to a theory is considered.
Keywords
Cite
@article{arxiv.0910.1735,
title = {The Cosmological constant and the Wheeler-DeWitt Equation},
author = {Remo Garattini},
journal= {arXiv preprint arXiv:0910.1735},
year = {2011}
}
Comments
Some misprints corrected. LaTeX 9 pages. Contribution given for the Workshop on Continuum and Lattice Approaches to Quantum Gravity. Sept. 2008, Brighton UK. To appear in the Proceedings