Cosmological Constant Problems and Renormalization Group

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The Cosmological Constant Problem emerges when Quantum Field Theory is applied to the gravitational theory, due to the enormous magnitude of the induced energy of the vacuum. The unique known solution of this problem involves an extremely precise fine-tuning of the vacuum counterpart. We review a few of the existing approaches to this problem based on the account of the quantum (loop) effects and pay special attention to the ones involving the renormalization group.
12 pages, LaTeX, based on the on the talk at IRGAC-2006 (Barcelona, July 11-15, 2006), misprints corrected, comment on anthropic approach modified, some references added, accepted in Journal of Physics A

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