The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization
Abstract
We discuss the case of massive gravitons and their relation with the cosmological constant, considered as an eigenvalue of a Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.
Keywords
Cite
@article{arxiv.gr-qc/0510061,
title = {The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization},
author = {Remo Garattini},
journal= {arXiv preprint arXiv:gr-qc/0510061},
year = {2009}
}
Comments
8 pages, Talk given at "QFEXT'05", the 7-th workshop on quantum field theory under the influence of external conditions, Barcelona, Spain, Sept. 5-9, 2005