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.

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

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• Cosmological Constant - the Weight of the Vacuum
• New Developments in the Casimir Effect
• No Van Dam-Veltman-Zakharov Discontinuity in Ads Space
• Quantum discontinuity between zero and infinitesimal graviton mass with a Lambda term
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