Introduction to Loop Quantum Cosmology
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and midisuperspace models as well as homogeneous and inhomogeneous effective dynamics.
gr-qc↗
arXiv subjects
Kinjal Banerjee
Publications and source records attributed to Kinjal Banerjee.
Some Aspects of Holst and Nieh-Yan Terms in General Relativity with Torsion
We explore the relation of the Holst term with the Nieh-Yan term in terms of metric variables. We show that the Holst term indeed affects the classical equations of motion in the presence of matter with spin. Therefore the correct term to add to the Einstein-Hilbert action such that the equations of motion are not affected is the Nieh-Yan term. We then calculate the torsion charge due to this term in the context of a perfect fluid sphere with torsion and show that it vanishes once a horizon is formed but not otherwise. We also show that adding on torsion to General Relativity the Einstein's equations are no longer holographic in torsion although they continue to be so for the metric.
gr-qc↗
Semiclassical environment of collapsing shells
We explore in detail the semiclassical environment of collapsing shells of matter, and determine the semiclassical flux measured by a variety of observers. This study is a preliminary step in a broader investigation of thermodynamic properties of the geometry of collapsing objects. Specifically, in this paper we consider spherically symmetric null and timelike collapsing shells which form an event horizon, and calculate the flux measured by observers both inside and outside the shell, and both inside and outside the event horizon, and find nontrivial results in most of the cases. Additionally, we also investigate the environment of a shell which collapses but \emph{does not} form a horizon, halting at some radius larger than the Schwarzschild radius, and find that such an object generically gives rise to a pulse of radiation which is sharply peaked as it travels inwards and is reflected at the origin, and eventually emerges from the shell in a "thermalized" form. Our results have potential consequences in addressing questions pertaining, e.g. to black hole entropy and backreaction.
gr-qc↗
Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is straightforward. Imposition of the Gauss constraint can be done on the kinematical Hilbert space to select subspace of gauge invariant states. We carry out the quantization of the Hamiltonian constraint making specific choices. Alternative choices are briefly discussed. It appears that to get spatial correlations reflected in the Hamiltonian constraint, one may have to adopt the so called `effective operator viewpoint'.
gr-qc↗
Loop Quantization of Polarized Gowdy Model on $T^3$: Classical Theory
The vacuum Gowdy models provide much studied, non-trivial midi-superspace examples. Various technical issues within Loop Quantum Gravity can be studied in these models as well as one can hope to understand singularities and their resolution in the loop quantization. The first step in this program is to reformulate the model in real connection variables in a manner that is amenable to loop quantization. We begin with the unpolarized model and carry out a consistent reduction to the polarized case. Carrying out complete gauge fixing, the known solutions are recovered.
gr-qc↗
Discreteness Corrections to the Effective Hamiltonian of Isotropic Loop Quantum Cosmology
One of the qualitatively distinct and robust implication of Loop Quantum Gravity (LQG) is the underlying discrete structure. In the cosmological context elucidated by Loop Quantum Cosmology (LQC), this is manifested by the Hamiltonian constraint equation being a (partial) difference equation. One obtains an effective Hamiltonian framework by making the continuum approximation followed by a WKB approximation. In the large volume regime, these lead to the usual classical Einstein equation which is independent of both the Barbero-Immirzi parameter $γ$ as well as $\hbar$. In this work we present an alternative derivation of the effective Hamiltonian by-passing the continuum approximation step. As a result, the effective Hamiltonian is obtained as a close form expression in $γ$. These corrections to the Einstein equation can be thought of as corrections due to the underlying discrete (spatial) geometry with $γ$ controlling the size of these corrections. These corrections imply a bound on the rate of change of the volume of the isotropic universe. In most cases these are perturbative in nature but for cosmological constant dominated isotropic universe, there are significant deviations.
gr-qc↗
Phase transitions in a network with range dependent connection probability
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-δ}$ in addition to nearest neighbour connections. This system has been shown to exhibit small world behaviour for $δ< 2$ above which its behaviour is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at $δ= 1$. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicate that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behaviour of a single quantity, the average bond length. The phase transitions in all dimensions are non-trivial in nature.
cond-mat.stat-mech↗