Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

Dumitru Baleanu
  • 1 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Çankaya University, 06530, Ankara, Turkey
  • 2 Institute of Space Sciences, R 76900, Magurele-Bucharest, Romania


The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] T. Tanaka and M. Sasaki: “No supercritical supercurvature mode conjecture in one-bubble open inflation”, Phys. Rev. D, Vol. 59, (1999), art. 023506.

  • [2] G. Lavrelashvili: “Quadratic action of the Hawking-Turok instanton”, Phys. Rev. D, Vol. 58, (1998), art. 063505.

  • [3] V.F. Mukhanov, H.A. Feldmann and R.H. Brandernerg: “Theory of cosmological perturbations”, Phys. Rep., Vol. 215, (1992), pp. 203–333.

  • [4] J. Garriga, X. Montes, M. Sasaki and T. Tanaka: “Canonical quantization of cosmological perturbations in the one-bubble open universe”, Nucl. Phys. B Vol. 513, (1998), pp. 343–374.

  • [5] S. Gratton and N. Turok: “Cosmological perturbations from the no boundary Euclidean path integral”, Phys. Rev. D, Vol. 60, (1999), art. 123507.

  • [6] P.A.M. Dirac: Lectures on Quantum Mechanics, Yeshiva University Press, New York, 1967.

  • [7] M. Henneaux and C. Teitelboim: Quantization of Gauge Systems, Princeton Univ. Press, 1992.

  • [8] A. Khvedelidze, G. Lavrelashvili and T. Tanaka: “Cosmological perturbations in a Friedmann-Robertson-Walker model with a scalar field and false vacuum decay”, Phys. Rev. D, Vol. 62, (2000), art. 083501.

  • [9] G.V. Lavrelashvili, V.A. Rubakov and P.G. Tinyakov: “Tunneling transitions with gravitation: Breakdown of the quasiclassical approximation”, Phys. Lett. B, Vol. 161, (1985), pp. 280–284.

  • [10] C.M. Amaral: “Configuration space constraints as projectors in the many-body system”, Nuovo Cimento B, Vol. 25(2), (1975), pp. 817–827.

  • [11] P. Pitanga: “Symplectic projector in constrained systems”, Nuovo Cimento A, Vol. 103, (1990), pp. 1529–1535.

  • [12] L.R.U. Manssur, A.L.M.A. Nogueira and M.A. Santos: “An extended Abelian Chern-Simons model and the symplectic projector method”, Int. J. Mod. Phys. A, Vol. 17(14), (2002), pp. 1919–1929.

  • [13] M.A. De Andrade, M.A. Santos and I.V. Vancea: “Local physical coordinates from symplectic projector method”, Mod. Phys. Lett. A, Vol. 16(29), (2001), pp. 1907–1917.

  • [14] H. De Cicco and C. Simeone: “Gauge invariance of parametrized systems and path integral quantization”, Int. J. Mod. Phys. A, Vol. 14, (1999), pp. 5105–5120; C. Simeone: “Gauge fixation and global phase time for minisuperspaces”, J. Math. Phys., Vol. 40, (1999), pp. 4527–4537; M. Henneaux, C. Teitelboim and T. Vergara: “Gauge fixation and global phase time for minisuperspaces”, Nucl. Phys. B, Vol. 387, (1992), pp. 391–419.

  • [15] C. Carathéodory: Calculus of Variations and Partial Differential Equations of the First Order, Part II, Holden-Day, 1967.

  • [16] B.M. Pimentel, R.G. Teixteira and J.L. Tomazelli: “Hamilton-Jacobi approach to Berezinian singular systems”, Ann. Phys., Vol. 267, (1998), pp. 75–96.

  • [17] S.I. Muslih and Y. Güler: “Is gauge fixing of constrained systems necessary?”, Nuovo Cimento B, Vol. 113, (1998), pp. 277–289.

  • [18] D. Baleanu and Y. Güler: “Hamilton-Jacobi treatment of a non-relativistic particle on a curved space”, J. Phys. A: Math. Gen., Vol. 34(1), (2001), pp. 73–80.

  • [19] D. Baleanu and Y. Güler: “Multi-Hamilton-Jacobi quantization of O(3) nonlinear sigma model”, Mod. Phys. Lett. B, Vol. 16(13), (2001), pp. 873–879.

  • [20] D. Baleanu and Y. Güler: “The Hamilton-Jacobi treatment of supersymmetric quantum mechanics”, Int. J. Mod. Phys. A, Vol. 16(13), 2001, pp. 2391–2397.

  • [21] B.M. Pimentel, P.J. Pompeia and J.F. da Rocha-Neto: “The Hamilton-Jacobi Approach to Teleparallelism”, Nuovo Cimento B, Vol. 120, (2005), pp. 981–992.

  • [22] B.M. Pimentel, P.J. Pompeia, J.F. da Rocha-Neto and R.G. Teixeira: “The Teleparallel Lagrangian and Hamilton-Jacobi formalism”, Gen. Rel. Grav., Vol. 35(5), (2003), pp. 877–884.

  • [23] D. Baleanu: “Reparametrization invariance and Hamilton-Jacobi formalism”, Nuovo Cimento B, Vol. 118(1), (2004), pp. 89–95.


Journal + Issues