Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-11-12
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Proceedings of the Conference "The Invisible Universe" Paris, June 29-July 3, 2009 10 pages
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 de Sitter and Anti-de Sitter 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 is used to handle with divergences. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. We apply this procedure on the induced cosmological constant $\Lambda$ and, as an alternative, on the Newton constant $G$. A brief discussion on the extension to a $f(R)$ theory is considered.
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