Abstract
Causal Dynamical Triangulations (CDT) is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are solely characterized by the discretized spatial volume. Using Monte Carlo simulations we determine the effective transfer matrix elements and extract the effective action for the scale factor. In this framework no degrees of freedom are frozen, however, the obtained action agrees with the minisuperspace model.
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Notes
- 1.
We slightly modified the form of the potential term. Such parametrization is more convenient to extract the parameters of the action.
References
Ambjørn, J., Jurkiewicz, J., Loll, R.: Dynamically triangulating Lorentzian quantum gravity. Nucl. Phys. B 610, 347 (2001). doi:10.1016/S0550-3213(01)00297-8
Ambjørn, J., Jurkiewicz, J., Loll, R.: Reconstructing the universe. Phys. Rev. D 72, 064014 (2005). doi:10.1103/PhysRevD.72.064014
Görlich, A.: Background geometry in 4D causal dynamical triangulations. Acta Phys. Pol. B 39, 3343 (2008)
Ambjørn, J., Görlich, A., Jurkiewicz, J., Loll, R.: Planckian birth of the quantum de Sitter universe. Phys. Rev. Lett. 100, 091304 (2008). doi:10.1103/PhysRevLett.100.091304
Ambjørn, J., Gizbert-Studnicki, J., Görlich, A., Jurkiewicz, J.: The transfer matrix in fourdimensional CDT. J. High Energy Phys. 2012(09), 017 (2012). doi:10.1007/JHEP09(2012)017
Ambjørn, J., Görlich, A., Jurkiewicz, J., et al.: The semiclassical limit of causal dynamical triangulations. Nucl. Phys. B 849, 144 (2011). doi:10.1016/j.nuclphysb.2011.03.019
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Görlich, A. (2014). The Transfer Matrix in Four-Dimensional Causal Dynamical Triangulations. In: Bičák, J., Ledvinka, T. (eds) Relativity and Gravitation. Springer Proceedings in Physics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-06761-2_71
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DOI: https://doi.org/10.1007/978-3-319-06761-2_71
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