Specific entropy as a clock for the evolutionary quantization of the isotropic Universe
- PDF / 968,934 Bytes
- 12 Pages / 595.276 x 790.866 pts Page_size
- 37 Downloads / 170 Views
Regular Article - Theoretical Physics
Specific entropy as a clock for the evolutionary quantization of the isotropic Universe Andrea Campolongo1,a , Giovanni Montani1,2,b 1 2
Dipartimento di Fisica, Università degli Studi di Roma “Sapienza”, Piazzale Aldo Moro 5, 00185 Rome, Italy Fusion and Nuclear Safety Department, ENEA C.R. Frascati, via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Received: 15 April 2020 / Accepted: 12 October 2020 © The Author(s) 2020
Abstract In this paper, we analyze the dynamics of an isotropic closed Universe in presence of a cosmological constant term and we compare its behavior in the standard Wheeler–DeWitt equation approach with the one when a Lagrangian fluid is considered in the spirit of the Kuchar– Brown paradigm. In particular, we compare the tunnelling of the Universe from the classically forbidden region to the allowed one, showing that considering a time evolution deeply influences the nature of the model. In fact, we show that in the presence of the Lagrangian fluid, the cosmological singularity is restored both in the classical and the quantum regime. However, in the quantum regime the singularity is probabilistically suppressed for some energy eigenvalues and in the case the latter is equal to zero one recovers the standard WDW case. Finally, we introduce a cut-off physics feature in the Minisuperspace by considering a Polymer quantum mechanical approach limiting our attention to the semi-classical dynamics mainly (the quantum treatment is inhibited by the non-local nature of the Hamiltonian operator). We show that the singularity is again removed, like in the fluid-free model, and a bouncing cosmology emerges so that the present model could mimic a cyclic cosmology.
1 Introduction One of the most puzzling questions of the canonical quantization of gravity is the so-called frozen formalism, i.e. the absence of an external time parameter for the quantum dynamics of the 3-metric field [1–4]. Furthermore, while the Loop Quantum Gravity implementation to cosmology leads to the existence of a Big-Bounce [5], the Wheeler–DeWitt equation, associated to a metric approach, seems, in general unable to remove the cosmological singularity on a quantum a e-mail:
[email protected] (corresponding author)
b e-mail:
[email protected]
0123456789().: V,-vol
level [6,7]. The main reason for the quantum survival of the cosmological singularity consists of the time-like character of the Universe volume in the Wheeler Super-space [8,9]. In fact, the Wheeler–DeWitt equation resembles a functional Klein–Gordon equation for which the 3-metric determinant behaves like an internal clock. As a result, all the values of this quantity are available to the dynamics, including its vanishing character, associated to the singularity. This feature is deeply altered in Loop Quantum Gravity since the 3-volume acquires a discrete spectrum. A non-singular Universe can be easily obtained in the Einsteinian dynamics if we include a positive cosmological constant into the evolution of an
Data Loading...
