The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization

Details The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization

2005-10-13

arxiv.org/abs/gr-qc/0510061v1

J.Phys. A39 (2006) 6393-6400

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, Talk given at "QFEXT'05", the 7-th workshop on quantum field theory under the influence of external conditions, Barce

Scientific paper

10.1088/0305-4470/39/21/S33

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.

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