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the cosmological constant from the wheeler de witt equation

2. The Cosmological Constant Problem. At the Planck era. For a pioneering review on this problem see S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).For more recent and detailed reviews see V. Sahni and A. Starobinsky, Int. J. Mod. Phys.D 9, 373 (2000), astro-ph/9904398; N. Straumann, The history of the cosmologicalconstant problem gr-qc/0208027; T.Padmanabhan, Phys.Rept. 380, 235 (2003),hep-th/0212290..

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the cosmological constant from the wheeler de witt equation

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    1. The Cosmological Constant from the Wheeler De Witt Equation Remo Garattini Università di Bergamo I.N.F.N. - Sezione di Milano

    2. 2 The Cosmological Constant Problem At the Planck era

    3. 3 Wheeler-De Witt Equation B. S. DeWitt, Phys. Rev.160, 1113 (1967).

    4. 4 Re-writing the WDW equation Where

    5. 5 Eigenvalue problem

    6. 6 Form of the background

    7. 7 Canonical Decomposition h is the trace (spin 0) (Lx)ij is the gauge part [spin 1 (transverse) + spin 0 (longitudinal)] h^ij represents the transverse-traceless component of the perturbation ? graviton (spin 2)

    8. 8

    9. 9 Graviton Contribution

    10. 10 Regularization

    11. 11

    12. 12 Renormalization Bare cosmological constant changed into

    13. 13 Renormalization Group Equation Eliminate the dependance on m and impose

    14. 14 Energy Minimization (L Maximization) At the scale m0

    15. 15 De Sitter Case

    16. 16 Extension to f(R) Theories[S. Capozziello and R.G., Class. Quant. Grav., 24, 1627 (2007)] A straightforward generalization is a f(R) theory substituting the classical Lagrangian with

    17. 17

    18. 18

    19. 19 De Sitter Case for a f(R) Theory

    20. 20 AdS Case for a f(R) Theory

    21. 21 Conclusions, Problems and Outlook Analysis to be completed. Beyond the W.K.B. approximation of the Lichnerowicz spectrum. Discrete Lichnerowicz spectrum. Introducing massive graviton. In progress, spectrum of spherically symmetric metrics

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