Casimir Energy of the Universe and the Dark Energy Problem

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.

12 pages, 13 figures, Proceedings of DSU2011(2011.9.26-30,Beijin)

References in corpus (8)

• On the Origin of Gravity and the Laws of Newton
• Thermodynamical Aspects of Gravity: New insights
• De Sitter Space and Eternity
• Decay of Vacuum Energy
• Casimir Energy of 5D Electro-Magnetism and Sphere Lattice Regularization
• Field Quantization in 5D Space-Time with Z${}_2$-parity and Position/Momentum Propagator
• Casimir Energy of 5D Electromagnetism and New Regularization Based on Minimal Area Principle
• Casimir Energy of AdS5 Electromagnetism and Cosmological Constant Problem