Note about canonical formalism for normalized gravity and vacuum energy sequestering model

Open Access
Regular Article - Theoretical Physics

Abstract

This short note is devoted to the Hamiltonian analysis of the normalized general relativity and recently proposed model of vacuum energy sequestering. The common property of these models is the presence of the global variables. We discuss the meaning of these global variables in the context of the canonical formalism and argue that their presence lead to the non-local form of the Hamiltonian constraint.

Keywords

Classical Theories of Gravity Models of Quantum Gravity 

References

  1. [1]
    S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys. 61 (1989) 1 [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  2. [2]
    E.J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15 (2006) 1753 [hep-th/0603057] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  3. [3]
    C.J. Isham and K.V. Kuchar, Representations of Space-time Diffeomorphisms. 2. Canonical Geometrodynamics, Annals Phys. 164 (1985) 316 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    C.J. Isham and K.V. Kuchar, Representations of Space-time Diffeomorphisms. 1. Canonical Parametrized Field Theories, Annals Phys. 164 (1985) 288 [INSPIRE].ADSCrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    E. Gourgoulhon, 3+1 formalism and bases of numerical relativity, gr-qc/0703035 [INSPIRE].
  6. [6]
    G.F.R. Ellis, H. van Elst, J. Murugan and J.-P. Uzan, On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity, Class. Quant. Grav. 28 (2011) 225007 [arXiv:1008.1196] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    G.F.R. Ellis, The Trace-Free Einstein Equations and inflation, Gen. Rel. Grav. 46 (2014) 1619 [arXiv:1306.3021] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Padilla and I.D. Saltas, A note on classical and quantum unimodular gravity, arXiv:1409.3573 [INSPIRE].
  9. [9]
    C. Gao, R.H. Brandenberger, Y. Cai and P. Chen, Cosmological Perturbations in Unimodular Gravity, arXiv:1405.1644 [INSPIRE].
  10. [10]
    P. Jain, A. Jaiswal, P. Karmakar, G. Kashyap and N.K. Singh, Cosmological implications of unimodular gravity, JCAP 11 (2012) 003 [arXiv:1109.0169] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    L. Smolin, Unimodular loop quantum gravity and the problems of time, Phys. Rev. D 84 (2011) 044047 [arXiv:1008.1759] [INSPIRE].ADSGoogle Scholar
  12. [12]
    L. Smolin, The Quantization of unimodular gravity and the cosmological constant problems, Phys. Rev. D 80 (2009) 084003 [arXiv:0904.4841] [INSPIRE].ADSMathSciNetGoogle Scholar
  13. [13]
    M. Shaposhnikov and D. Zenhausern, Scale invariance, unimodular gravity and dark energy, Phys. Lett. B 671 (2009) 187 [arXiv:0809.3395] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  14. [14]
    E. Alvarez, Can one tell Einsteins unimodular theory from Einsteins general relativity?, JHEP 03 (2005) 002 [hep-th/0501146] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    D.R. Finkelstein, A.A. Galiautdinov and J.E. Baugh, Unimodular relativity and cosmological constant, J. Math. Phys. 42 (2001) 340 [gr-qc/0009099] [INSPIRE].
  16. [16]
    C. Barceló, R. Carballo-Rubio and L.J. Garay, Unimodular gravity and general relativity from graviton self-interactions, Phys. Rev. D 89 (2014) 124019 [arXiv:1401.2941] [INSPIRE].ADSGoogle Scholar
  17. [17]
    C. Barceló, R. Carballo-Rubio and L.J. Garay, Absence of cosmological constant problem in special relativistic field theory of gravity, arXiv:1406.7713 [INSPIRE].
  18. [18]
    A.A. Tseytlin, Duality symmetric string theory and the cosmological constant problem, Phys. Rev. Lett. 66 (1991) 545 [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Davidson and S. Rubin, Normalized general relativity: Nonclosed universe and a zero cosmological constant, Phys. Rev. D 89 (2014) 024036 [arXiv:1401.8113] [INSPIRE].ADSGoogle Scholar
  20. [20]
    A. Davidson and S. Rubin, Zero Cosmological Constant from Normalized General Relativity, Class. Quant. Grav. 26 (2009) 235019 [arXiv:0905.0661] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  21. [21]
    N. Kaloper and A. Padilla, Sequestering the Standard Model Vacuum Energy, Phys. Rev. Lett. 112 (2014) 091304 [arXiv:1309.6562] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    N. Kaloper and A. Padilla, Vacuum Energy Sequestering: The Framework and Its Cosmological Consequences, Phys. Rev. D 90 (2014) 084023 [arXiv:1406.0711] [INSPIRE].ADSGoogle Scholar
  23. [23]
    N. Kaloper and A. Padilla, ’The End’, arXiv:1409.7073 [INSPIRE].
  24. [24]
    J. Govaerts, The Quantum geometers universe: Particles, interactions and topology, hep-th/0207276 [INSPIRE].
  25. [25]
    M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton, Univ. Pr., 1992, pg. 520, U.S.A.Google Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Theoretical Physics and Astrophysics, Faculty of ScienceMasaryk UniversityBrnoCzech Republic

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