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

Remo Garattini
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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.

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Remo Garattini. 2005-10-13. The Cosmological Constant as an Eigenvalue of a Sturm-Liouville Problem and its Renormalization. https://doi.org/10.1088/0305-4470%2F39%2F21%2Fs33

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