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arXiv · 1205.1316

Casimir Energy of the Universe and the Dark Energy Problem

Shoichi Ichinose
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Abstract

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function ($\be$-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.

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Shoichi Ichinose. 2012-05-07. Casimir Energy of the Universe and the Dark Energy Problem. https://doi.org/10.1088/1742-6596/384/1/012028

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