arXiv subjects

Ghanashyam Date

Publications and source records attributed to Ghanashyam Date.

28 records · Page 2Linked to original sources

arXiv2005

Absence of the Kasner singularity in the effective dynamics from loop quantum cosmology

In classical general relativity, the generic approach to the initial singularity is usually understood in terms of the BKL scenario. In this scenario, along with the Bianchi IX model, the exact, singular, Kasner solution of vacuum Bianchi I model also plays a pivotal role. Using an effective classical Hamiltonian obtained from loop quantization of vacuum Bianchi I model, exact solution is obtained which is non-singular due to a discreteness parameter. The solution is parameterized in exactly the same manner as the usual Kasner solution and reduces to the Kasner solution as discreteness parameter is taken to zero. At the effective Hamiltonian level, the avoidance of Kasner singularity uses a mechanism distinct from the `inverse volume' modifications characteristic of loop quantum cosmology.

gr-qc↗

arXiv2005

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↗

arXiv2004

Genericness of inflation in isotropic loop quantum cosmology

Non-perturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector is already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semi-definite potentials it is always possible to choose, without fine tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with generic occurrence of bounce at small volumes, particle horizon is absent thus eliminating the horizon problem of the standard Big Bang model.

gr-qc↗

arXiv2004

Genericness of Big Bounce in isotropic loop quantum cosmology

The absence of isotropic singularity in loop quantum cosmology can be understood in an effective classical description as the universe exhibiting a Big Bounce. We show that with scalar matter field, the big bounce is generic in the sense that it is independent of quantization ambiguities and details of scalar field dynamics. The volume of the universe at the bounce point is parametrized by a single parameter. It provides a minimum length scale which serves as a cut-off for computations of density perturbations thereby influencing their amplitudes.

gr-qc↗

arXiv2004

Effective Hamiltonian for Isotropic Loop Quantum Cosmology

For a class of solutions of the fundamental difference equation of isotropic loop quantum cosmology, the difference equation can be replaced by a differential equation valid for {\em all} values of the triad variable. The differential equation admits a `unique' non-singular continuation through vanishing triad. A WKB approximation for the solutions leads to an effective continuum Hamiltonian. The effective dynamics is also non-singular (no big bang singularity) and approximates the classical dynamics for large volumes. The effective evolution is thus a more reliable model for further phenomenological implications of the small volume effects.

gr-qc↗

arXiv2004

ICGC-2004 Conference Overview

This is a written, expanded version of the summary talk given at the conclusion of the ICGC-2004 held at Cochin. Brief introductory remarks are included to provide a slightly wider context to the theme talks.

gr-qc↗

arXiv2004

The Bianchi IX model in Loop Quantum Cosmology

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities.

gr-qc↗

arXiv2004

Quantum suppression of the generic chaotic behavior close to cosmological singularities

In classical general relativity, the generic approach to the initial singularity is very complicated as exemplified by the chaos of the Bianchi IX model which displays the generic local evolution close to a singularity. Quantum gravity effects can potentially change the behavior and lead to a simpler initial state. This is verified here in the context of loop quantum gravity, using methods of loop quantum cosmology: the chaotic behavior stops once quantum effects become important. This is consistent with the discrete structure of space predicted by loop quantum gravity.

gr-qc↗

arXiv2004

Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection

Homogeneous cosmological models with non-vanishing intrinsic curvature require a special treatment when they are quantized with loop quantum cosmological methods. Guidance from the full theory which is lost in this context can be replaced by two criteria for an acceptable quantization, admissibility of a continuum approximation and local stability. A quantization of the corresponding Hamiltonian constraints is presented and shown to lead to a locally stable, non-singular evolution compatible with almost classical behavior at large volume. As an application, the Bianchi IX model and its modified behavior close to its classical singularity is explored.

gr-qc↗

arXiv2003

Consistency Conditions for Fundamentally Discrete Theories

The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to ensure that the numerical solutions can reliably be used as approximations to solutions of the differential equation. There are, however, also systems where a difference equation is deemed to be fundamental, mainly in the context of quantum gravity. Since difference equations in general are harder to solve analytically than differential equations, it can be helpful to introduce an approximating differential equation as a continuum approximation. In this paper implications of this change in view point are analyzed to derive the conditions that the difference equation should satisfy. The difference equation in such a situation cannot be chosen freely but must be derived from a fundamental theory. Thus, the conditions for a discrete formulation can be translated into conditions for acceptable quantizations. In the main example, loop quantum cosmology, we show that the conditions are restrictive and serve as a selection criterion among possible quantization choices.

gr-qc↗