Stephani-Schutz quantum cosmology

We study the Stephani quantum cosmological model in the presence of a cosmological constant in radiation dominated Universe. In the present work the Schutz's variational formalism which recovers the notion of time is applied. This gives rise to Wheeler-DeWitt equations which can be cast in the form of Schr\"odinger equations for the scale factor. We find their eigenvalues and eigenfunctions by using the Spectral Method. Then we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor, which is found to oscillate between non-zero finite maximum and minimum values. Since the expectation value of the scale factor never tends to the singular point, we have an initial indication that this model may not have singularities at the quantum level.Comment: 6 pages, 4 figures, 1 table, to appear in PL

Gravitational wave sources: An overview

With full-sensitivity operation of the first generation of gravitational wave detectors now just around the corner, and with the LISA space-based detector entering its final design stage, I review the wide variety of predicted sources from the perspective of what further theoretical work may be needed to assist in their detection. Some sources, such as binary black holes, require good theoretical models from which search templates for matched filtering of the data streams can be computed. Others, such as searches for un-modelled bursts, require clever robust search algorithms not tied to detailed waveform models. Still others, such as searches for continuous waves from pulsars, are compute-bound and need improved efficient computer algorithms. The sensitivity of initial ground-based detectors will depend in part on how good we are at searching the data. In the longer term, the amount of information we can extract from the LISA data stream will depend in part on how good we are at removing strong signals so that we can recover the weaker ones as well

Competition with Exclusive Contracts in Vertically Related Markets: An Equilibrium Non-Existence Result

I develop a model in the spirit of Ordover, Saloner, and Salop (1990), in which two upstream firms compete to supply a homogeneous input to two downstream firms, who compete in prices with differentiated products in a downstream market. Upstream firms are allowed to offer exclusive two-part tariff contracts to the downstream firms. I show that, under very general conditions, this game does not have a subgame-perfect equilibrium in pure strategies. The intuition is that variable parts in such an equilibrium would have to be pairwise-proof. But when variable parts are pairwise-proof, downstream competitive externalities are not internalized, and there exists a profitable deviation. I contrast this non-existence result with earlier papers that found equilibria in similar models

Standing in the Dark: Sloth and Stability, Paralysis and Perseverance in Book IV of the Confessio Amantis

In Book IV of the Confessio, things happen in the dark – the dark of night, of dreams, of despair, of secrecy, of treachery, of death. The medieval sin of accidia sets the pace for this beautifully constructed book, whose tales link and cross, as in a dance. Dido, Phyllis, the bad, the forgetful, and the obsessive lovers swing like slowing pendulums back to their starting points, and stop still. On the whole, their dance with Amans is a slow and stately pavane of the dead and desperate. This is Gower’s darkest book, though not the most bloody: Sloth is a sin of failure. Consequently, Book IV is interested in stones, especially statues, an aesthetic harmony between poetry and poetics which cannot be ignored. Statuary – as creation, as punishment, as static, as dynamic – grounds a complex and subtle discussion about stability, and stasis, perseverance and paralysis, beauty and monstrosity. This paper examines the paradoxes and thematic clusters arising out of the suicides and culminating in Araxarathen’s voluntary transformation to stone

Classical and quantum cosmology of minimal massive bigravity

In a Friedmann-Robertson-Walker (FRW) space-time background we study the classical cosmological models in the context of recently proposed theory of nonlinear minimal massive bigravity. We show that in the presence of perfect fluid the classical field equations acquire contribution from the massive graviton as a cosmological term which is positive or negative depending on the dynamical competition between two scale factors of bigravity metrics. We obtain the classical field equations for flat and open universes in the ordinary and Schutz representation of perfect fluid. Focusing on the Schutz representation for flat universe, we find classical solutions exhibiting singularities at early universe with vacuum equation of state. Then, in the Schutz representation, we study the quantum cosmology for flat universe and derive the Schrodinger-Wheeler-DeWitt equation. We find its exact and wave packet solutions and discuss on their properties to show that the initial singularity in the classical solutions can be avoided by quantum cosmology. Similar to the study of Hartle-Hawking no-boundary proposal in the quantum cosmology of de Rham, Gabadadze and Tolley (dRGT) massive gravity, it turns out that the mass of graviton predicted by quantum cosmology of the minimal massive bigravity is large at early universe. This is in agreement with the fact that at early universe the cosmological constant should be large.Comment: 13 pages, 6 figures, published online, Phys. Lett. B (2016

The art and science of black hole mergers

The merger of two black holes is one of the most extraordinary events in the natural world. Made of pure gravity, the holes combine to form a single hole, emitting a strong burst of gravitational radiation. Ground-based detectors are currently searching for such bursts from holes formed in the evolution of binary stars, and indeed the very first gravitational wave event detected may well be a black-hole merger. The space-based LISA detector is being designed to search for such bursts from merging massive black holes in the centers of galaxies, events that would emit many thousands of solar masses of pure gravitational wave energy over a period of only a few minutes. To assist gravitational wave astronomers in their searches, and to be in a position to understand the details of what they see, numerical relativists are performing supercomputer simulations of these events. I review here the state of the art of these simulations, what we have learned from them so far, and what challenges remain before we have a full prediction of the waveforms to be expected from these events.Comment: 12 pages, 3 figures, Proceedings of "Growing Black Holes", Garching 21-25 June 200

Introduction to the Analysis of Low-Frequency Gravitational Wave Data

The space-based gravitational wave detector LISA will observe in the low-frequency gravitational-wave band (0.1 mHz up to 1 Hz). LISA will search for a variety of expected signals, and when it detects a signal it will have to determine a number of parameters, such as the location of the source on the sky and the signal's polarisation. This requires pattern-matching, called matched filtering, which uses the best available theoretical predictions about the characteristics of waveforms. All the estimates of the sensitivity of LISA to various sources assume that the data analysis is done in the optimum way. Because these techniques are unfamiliar to many young physicists, I use the first part of this lecture to give a very basic introduction to time-series data analysis, including matched filtering. The second part of the lecture applies these techniques to LISA, showing how estimates of LISA's sensitivity can be made, and briefly commenting on aspects of the signal-analysis problem that are special to LISA.Comment: 20 page

Binary neutron star inspiral, LIGO, and cosmology

Recent work on the expected event rate of neutron star inspiral signals in the LIGO detector is summarized. The observed signals will be from inspirals at cosmological distances, and the important cosmological effects on the event rate and spectrum are discussed. This paper is a contribution to the proceedings of the 17th Texas Symposium held in Munich, 12-17 December 1994.Comment: 4 pages, REVTeX3.x, no figure

Sources of radiation from neutron stars

I give a brief introduction to the problem of detecting gravitational radiation from neutron stars. After a review of the mechanisms by which such stars may produce radiation, I consider the different search strategies appropriate to the different kinds of sources: isolated known pulsars, neutron stars in binaries, and unseen neutron stars. The problem of an all-sky survey for unseen stars is the most taxing one that we face in analysing data from interferometers. I describe the kinds of hierarchical methods that are now being investigated to reach the maximal sensitivity, and I suggest a replacement for standard Fourier-transform search methods that requires fewer floating-point operations for Fourier-based searches over large parameter spaces, and in addition is highly parallelizable, working just as well on a loosely coupled network of workstations as on a tightly coupled parallel computer.Comment: 11 pages, no figure

Getting Ready for GEO600 Data

Data of good quality is expected from a number of gravitational wave detectors within the next two years. One of these, GEO600, has special capabilities, such as narrow-band operation. I describe here the preparations that are currently being made for the analysis of GEO600 data.Comment: 17 pages, 7 figures, proceedings of Yukawa International Seminar 199