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.Comment: revtex4, 4 pages, 5 figures. Published version. Title and abstract changed to match with the published version and Other minor changes. Conclusions unchange

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.Comment: 4 pages, revtex4, no figure

Pre-classical solutions of the vacuum Bianchi I loop quantum cosmology

Loop quantization of diagonalized Bianchi class A models, leads to a partial difference equation as the Hamiltonian constraint at the quantum level. A criterion for testing a viable semiclassical limit has been formulated in terms of existence of the so-called pre-classical solutions. We demonstrate the existence of pre-classical solutions of the quantum equation for the vacuum Bianchi I model. All these solutions avoid the classical singularity at vanishing volume.Comment: 4 pages, revtex4, no figures. In version 2, reference added and minor changes made. The final Version 3 includes additional explanation

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.Comment: 4 pages, revtex4, one figure. Only e-print archive numbers correctedi in the second version. Reference added in the 3rd version. Final version to appear in Phys. Rev. Lett. Explanations improve

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 $\gamma$ 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 $\gamma$. These corrections to the Einstein equation can be thought of as corrections due to the underlying discrete (spatial) geometry with $\gamma$ 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.Comment: Revtex4, 24 pages, 3 figures. In version 2, one reference and a para pertaining to it are added. In the version 3, some typos are corrected and remark 4 in section III is revised. Final version to appear in Class. Quantum Gra

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.Comment: 33 page

Loop Quantization of Polarized Gowdy Model on T3T^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.Comment: 20 pages, no figures. Final version; to appear in Classical and Quantum Gravity. Additional References include

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.Comment: revtex4, 36 pages, 10 figures. In version 2 the introduction is expanded, section III E is added and a paragraph on relevance of results is added in the conclusions. Refs updated, results unchanged. To appear in Class. Quant. Gravit

An efficient synthesis of open chain nitroalcohols by regioselective ring opening of cyclic tert-β-nitroalcohols by sodium borohydride: Short synthesis of (±)-tridecan-12-olide and (±)-9-tetradecanolide

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Activation of interferon-inducible 2′5′ oligoadenylate synthetase by adenoviral VAI RNA

2′-5′ oligoadenylate (2-5(A)) synthetase and protein kinase, RNA activated (PKR) are the only two known enzymes that bind double-stranded RNA (dsRNA) and get activated by it. We have previously identified their dsRNA binding domains, which do not have any sequence homology. Here, we report a profound difference between the two enzymes with respect to the structural features of the dsRNA that are required for their activation. The adenoviral virus-associated type I (VAI) RNA cannot activate PKR, although it binds to the protein and thereby prevents its activation by authentic dsRNA. In contrast, we observed that VAI RNA can both bind and activate 2-5(A) synthetase. Mutations in VAI RNA, which removed occasional mismatches present in its double-stranded stems, markedly enhanced its 2-5(A) synthetase-activating capacity. These mutants, however, are incapable of activating PKR. Other mutations, which disrupted the structure of the central stem-loop region of the VAI RNA, reduced its ability to activate 2-5(A) synthetase. These debilitated mutants could bind to the synthetase protein, although they fail to bind to PKR