Quantum cosmology of a classically constrained nonsingular Universe

The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been pointed out that, parameterization of classical trajectories with semiclassical time parameter, for such a classically constrained system, is a nontrivial task and requires Lagrangian formulation rather than the Hamiltonian formalism.Comment: 15 page

Entanglement entropy of black holes

The entanglement entropy is a fundamental quantity which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff which regulates the short-distance correlations. The geometrical nature of the entanglement entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in 4 and 6 dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as 't Hooft's brick wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields which non-minimally couple to gravity is emphasized. The holographic description of the entanglement entropy of the black hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.Comment: 89 pages; an invited review to be published in Living Reviews in Relativit

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit

Method of analysis of the spatial galaxy distribution at gigaparsec scales. I. Initial principles

Initial principles of a method of analysis of the luminous matter spatial distribution with sizes about thousands Mpc are presented. The method is based on an analysis of the photometric redshift distribution N(z) in the deep fields with large redshift bins \Deltaz=0.1{\div}0.3. Number density fluctuations in the bins are conditioned by the Poisson's noise, the correlated structures and the systematic errors of the photo-z determination. The method includes covering of a sufficiently large region on the sky by a net of the deep multiband surveys with the sell size about 10^{\circ}x10^{\circ} where individual deep fields have angular size about 10'x10' and may be observed at telescopes having diameters 3-10 meters. The distributions of photo-z within each deep field will give information about the radial extension of the super large structures while a comparison of the individual radial distributions of the net of the deep fields will give information on the tangential extension of the super large structures. A necessary element of the method is an analysis of possible distortion effects related to the methodic of the photo-z determination.Comment: 12 page

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

OneG: A Computational Tool for Predicting Cryptic Intermediates in the Unfolding Kinetics of Proteins under Native Conditions

Understanding the relationships between conformations of proteins and their stabilities is one key to address the protein folding paradigm. The free energy change (ΔG) of unfolding reactions of proteins is measured by traditional denaturation methods and native hydrogen-deuterium (H/D) exchange methods. However, the free energy of unfolding (ΔGU) and the free energy of exchange (ΔGHX) of proteins are not in good agreement, though the experimental conditions of both methods are well matching to each other. The anomaly is due to any one or combinations of the following reasons: (i) effects of cis-trans proline isomerisation under equilibrium unfolding reactions of proteins (ii) inappropriateness in accounting the baselines of melting curves (iii) presence of cryptic intermediates, which may elude the melting curve analysis and (iv) existence of higher energy metastable states in the H/D exchange reactions of proteins. Herein, we have developed a novel computational tool, OneG, which accounts the discrepancy between ΔGU and ΔGHX of proteins by systematically accounting all the four factors mentioned above. The program is fully automated and requires four inputs: three-dimensional structures of proteins, ΔGU, ΔGU* and residue-specific ΔGHX determined under EX2-exchange conditions in the absence of denaturants. The robustness of the program has been validated using experimental data available for proteins such as cytochrome c and apocytochrome b562 and the data analyses revealed that cryptic intermediates of the proteins detected by the experimental methods and the cryptic intermediates predicted by the OneG for those proteins were in good agreement. Furthermore, using OneG, we have shown possible existence of cryptic intermediates and metastable states in the unfolding pathways of cardiotoxin III and cobrotoxin, respectively, which are homologous proteins. The unique application of the program to map the unfolding pathways of proteins under native conditions have been brought into fore and the program is publicly available at http://sblab.sastra.edu/oneg.htm

PpiA, a Surface PPIase of the Cyclophilin Family in Lactococcus lactis

Background: Protein folding in the envelope is a crucial limiting step of protein export and secretion. In order to better understand this process in Lactococcus lactis, a lactic acid bacterium, genes encoding putative exported folding factors like Peptidyl Prolyl Isomerases (PPIases) were searched for in lactococcal genomes. Results: In L. lactis, a new putative membrane PPIase of the cyclophilin subfamily, PpiA, was identified and characterized. ppiA gene was found to be constitutively expressed under normal and stress (heat shock, H2O2) conditions. Under normal conditions, PpiA protein was synthesized and released from intact cells by an exogenously added protease, showing that it was exposed at the cell surface. No obvious phenotype could be associated to a ppiA mutant strain under several laboratory conditions including stress conditions, except a very low sensitivity to H2O2. Induction of a ppiA copy provided in trans had no effect i) on the thermosensitivity of an mutant strain deficient for the lactococcal surface protease HtrA and ii) on the secretion and stability on four exported proteins (a highly degraded hybrid protein and three heterologous secreted proteins) in an otherwise wild-type strain background. However, a recombinant soluble form of PpiA that had been produced and secreted in L. lactis and purified from a culture supernatant displayed both PPIase and chaperone activities. Conclusions: Although L. lactis PpiA, a protein produced and exposed at the cell surface under normal conditions, displaye