Nonperturbative analysis of the evolution of cosmological perturbations through a nonsingular bounce

In bouncing cosmology, the primordial fluctuations are generated in a cosmic contraction phase before the bounce into the current expansion phase. For a nonsingular bounce, curvature and anisotropy grow rapidly during the bouncing phase, raising questions about the reliability of perturbative analysis. In this paper, we study the evolution of adiabatic perturbations in a nonsingular bounce by nonperturbative methods including numerical simulations of the nonsingular bounce and the covariant formalism for calculating nonlinear perturbations. We show that the bounce is disrupted in regions of the universe with significant inhomogeneity and anisotropy over the background energy density, but is achieved in regions that are relatively homogeneous and isotropic. Sufficiently small perturbations, consistent with observational constraints, can pass through the nonsingular bounce with negligible alteration from nonlinearity. We follow scale invariant perturbations generated in a matter-like contraction phase through the bounce. Their amplitude in the expansion phase is determined by the growing mode in the contraction phase, and the scale invariance is well preserved across the bounce.Comment: 38 pages + appendices, 22 figure

Recent Cases: Wills — Descent of Insurance Proceeds Covering Extinguished Specific Bequests

Two recent cases involving the disposition of proceeds of insurance policies covering property given by specific bequest and destroyed immediately before testator\u27s death reach apparently opposite, but readily distinguishable, results. In a Kansas case a farmer had bequeathed his realty to his children and his personality to his wife. A tornado destroyed the farm buildings and fatally injured the farmer. Held: the proceeds from insurance covering the farm buildings descended to the heirs of the realty. An Oklahoma case involved the accidental destruction of an insured automobile and consequent death of its owner. Held: the insurance proceeds went to the legatee of the personal estate; only the wreckage of the automobile went to the legatee of the car. Both cases involved destruction of a specific bequest between the time of the execution of the will and death of the testator. In one the bequest was of personality; in the other it was of realty. Therein lies the distinction between the two cases and the basis for a reconciliation of their holdings

Oil and Gas—Effect of Entirety Clauses on Grantees Taking under Deeds Subject to Lease

Often the owner of land places it under an oil lease and later conveys fee interests or mineral or royalty interests in segregated tracts from the leased area. When oil is subsequently produced on some, but not all of the leased area, problems may arise as to the royalty rights of the lessor and the grantees. Specifically, is the right of each grantee to royalties modified by the fact that his tract is part of a larger leased area? The problem will be considered in the absence and in the presence of the contractual device known as the entirety clause. Various types of conveyances may give rise to this problem: conveyance of an interest in the fee; conveyance of an interest in the minerals under the land; or conveyance of an interest in royalties. Unless otherwise indicated, “conveyance” henceforth in this note will refer to conveyance of interest in the minerals

Recent Cases: Constitutional Law — Freedom of Speech — Conviction for Speaking After Having Been Wrongfully Denied License To Do So

Defendant, a Jehovah\u27s Witness, was convicted of conducting a public meeting in a city park without first obtaining the license re­quired by city ordinance. Defendant maintained that he had applied for such license, but had been wrongfully denied it. The New Hamp­shire Supreme Court held the ordinance valid, and the conviction binding, notwithstanding the wrongfulness of the refusal to grant the license. Upon appeal to the United States Supreme Court, held: conviction affirmed. The refusal to grant the license was a wrongful contravention of purely ministerial powers conferred by the ordinance; but such wrongfulness was no defense to defendant\u27s violation of the ordinance by proceeding with the speech. His only remedy would have been a mandamus action

On the relation of the gravitino mass and the GUT parameters

In this article we consider the local supersymmetry breaking and the broken SU(5) symmetry permisible by dilaton vacuum configuration in supergravity theories. We establish the parameter relation of spontaneuos breaking of supersymmetry and of the GUT theory.Comment: 12 pages, file written in Revtex forma

Scale invariance and critical gravitational collapse

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik critical solution. We find a different system, based on maximal slicing. This system does evolve periodically, and may generalize to the case of axisymmetry or of no symmetry at all.Comment: 7 pages, 3 figures, Revtex, discussion modified to clarify presentatio

Rapid Thermalization in Field Theory from Gravitational Collapse

Motivated by the duality with thermalization in field theory, we study gravitational collapse of a minimally coupled massless scalar field in Einstein gravity with a negative cosmological constant. We investigate the system numerically and establish that for small values of the initial amplitude of the scalar field there is no black hole formation, rather, the scalar field performs an oscillatory motion typical of geodesics in AdS. For large enough values of the amplitude of the scalar field we find black hole formation which we detect numerically as the emergence of an apparent horizon. Using the time of formation as an estimate for thermalization in the field theory we conclude that thermalization occurs very rapidly, close to the causal bound for a very wide range of black hole masses. We further study the thermalization time in more detail as a function of the amplitude and the width of the initial Gaussian scalar field profile and detect a rather mild structure.Comment: 5 pages, 4 figures. v2: References added, improved most grids by a factor of 8, main results unchanged. v3 PRD versio

Numerical simulations of general gravitational singularities

This paper covers some of the current techniques and issues involved in performing numerical simulations of the formation of singularities.Comment: This work was part of the 2006 AEI conference on New Frontiers in Numerical Relativity and was published in an issue of Classical and Quantum Gravity on that conferenc