Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1311.6004

Semiclassical and quantum behavior of the Mixmaster model in the polymer approach

Orchidea Maria Lecian·Giovanni Montani·Riccardo Moriconi
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete na- ture in the anisotropy variables of the Universe induces on the morphology of the cosmological sin- gularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB (Wentzel-Kramers-Brillouin) approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases, in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance, for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no longer chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility to remove the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the Mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universe anisotropy.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Orchidea Maria Lecian, Giovanni Montani, Riccardo Moriconi. 2013-11-23. Semiclassical and quantum behavior of the Mixmaster model in the polymer approach. https://doi.org/10.1103/physrevd.88.103511

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Naturally Light Distortion

In the most general formulation of gravity, the metric and connection are independent degrees of freedom, and the connection may include torsion and non-metricity (or distortion, collectively) degrees of freedom, resulting in a huge number of possible dynamical fields. However, most fields are either non-dynamical or extremely heavy and the general relativity is recovered at low energy. We find a unique naturally light vector- or scalar-like distortion field, which can be dynamical and have phenomenological implications. In particular, a light scalar particle that mixes with the Higgs boson naturally appears.

gr-qc↗
arXiv2026

Polarization-Dependent Photon Propagation, Quasinormal Modes, and Gravitational Lensing in Higher-Curvature Effective Theories

We investigate the impact of higher-curvature corrections on photon propagation within an effective field theory framework and their observational consequences in strong gravitational fields. We consider polarization-dependent modifications to photon trajectories in static and spherically symmetric spacetimes, focusing on Schwarzschild and Reissner--Nordström black hole backgrounds. Using the geometrical optics approximation, we derive the effective metrics governing photon propagation and study the resulting polarization-dependent shifts of the photon sphere. We compute the corresponding quasinormal modes in the eikonal limit and analyze their polarization dependence. We further investigate gravitational lensing, focusing on polarization-dependent corrections to the deflection angle in both weak- and strong-field regimes. In the strong-deflection regime, we find that even perturbatively small EFT corrections modify the coefficient of the logarithmically divergent part of the deflection angle, resulting in a potentially observable difference from the uncorrected case. This suggests that strong gravitational lensing may provide a sensitive probe of small higher-curvature corrections. While extracting EFT information directly from QNM frequencies is more subtle, QNMs may provide complementary information to gravitational lensing in future studies. Our results establish a framework for probing higher-curvature effects through polarization-dependent strong-field observables.

gr-qc↗
arXiv2026

Dynamics for Spin-$1/2$ Particles in Einstein-Gauss-Bonnet Gravity II: Non-Relativistic Case

In this work, I investigate the non-relativistic quantum dynamics of spin-1/2 particles in Einstein-Gauss-Bonnet (EGB) gravity and establish a direct connection between higher-curvature corrections, fermionic dynamics, and the phenomenology of compact objects. Starting from the Dirac Hamiltonian in a static, spherically symmetric EGB spacetime, we perform a Fold-Wouthuysen transformation and derive the effective Hamiltonian, including relativistic kinetic, gravitational, spin-orbit, and higher-curvature contributions. Heisenberg equations are then used to obtain the dynamics of velocity, force, and spin, revealing explicit EGB corrections for both translational motion and spin transport. In particular, the spin-orbit sector induces a modified precession frequency whose fractional deviation from general relativity scales as $δ_Ω=-4(ξ/M^{2})(M/ρ)^{3}$, providing a clear dimensionless signature of the Gauss-Bonnet coupling. Through Ehrenfest's theorem, we also establish the correspondence between the dynamics of quantum operators and their semiclassical gravitational limit. As an astrophysical application, we consider the stellar-mass black hole A0620-00 and show that prospective relative sensitivities in spin precession on the order of $10^{-3}$ to $10^{-4}$ can probe Gauss-Bonnet couplings in the range of approximately $10^{6}$ to $10^{8}\,{\rm m}^{2}$, depending on the orbital radius. This result identifies fermionic spin precession as a complementary channel for testing gravity with higher-curvature corrections and provides a quantum-mechanical framework connecting modified gravitational dynamics to precision phenomenology in strong-gravity regimes.

gr-qc↗