The Hubble series: Convergence properties and redshift variables

In cosmography, cosmokinetics, and cosmology it is quite common to encounter physical quantities expanded as a Taylor series in the cosmological redshift z. Perhaps the most well-known exemplar of this phenomenon is the Hubble relation between distance and redshift. However, we now have considerable high-z data available, for instance we have supernova data at least back to redshift z=1.75. This opens up the theoretical question as to whether or not the Hubble series (or more generally any series expansion based on the z-redshift) actually converges for large redshift? Based on a combination of mathematical and physical reasoning, we argue that the radius of convergence of any series expansion in z is less than or equal to 1, and that z-based expansions must break down for z>1, corresponding to a universe less than half its current size. Furthermore, we shall argue on theoretical grounds for the utility of an improved parameterization y=z/(1+z). In terms of the y-redshift we again argue that the radius of convergence of any series expansion in y is less than or equal to 1, so that y-based expansions are likely to be good all the way back to the big bang y=1, but that y-based expansions must break down for y<-1, now corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and Quantum Gravit

A Theoretical Construction of Thin Shell Wormhole from Tidal Charged Black hole

Recently, Dadhich et al [ Phys.Lett.B 487, 1 (2000)] have discovered a black hole solution localized on a three brane in five dimensional gravity in the Randall-Sundrum scenario. In this article, we develop a new class of thin shell wormhole by surgically grafting above two black hole spacetimes. Various aspects of this thin wormhole are also analyzed.Comment: 14 pages, 6 figures, Accepted in Gen.Rel.Gra

Riemannian geometry of irrotational vortex acoustics

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the ``acoustic geometry'' that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity $\Gamma/(2\pi cb)$, where $\Gamma$ is the vortex circulation, $c$ the speed of sound, and $b$ the impact parameter.Comment: 4 pages, 2 figures, RevTex4. Discussion of focal length added; to appear in Physical Review Letter

Sudden future singularities in FLRW cosmologies

The standard energy conditions of classical general relativity are applied to FLRW cosmologies containing sudden future singularities. Here we show, in a model independent way, that although such cosmologies can satisfy the null, weak and strong energy conditions, they always fail to satisfy the dominant energy condition. They require a divergent spacelike energy flux in all but the comoving frame.Comment: revtex4. Added references and a definition. To appear in CQ

Wormholes and Child Universes

Evidence to the case that classical gravitation provides the clue to make sense out of quantum gravity is presented. The key observation is the existence in classical gravitation of child universe solutions or "almost" solutions, "almost" because of some singularity problems. The difficulties of these child universe solutions due to their generic singularity problems will be very likely be cured by quantum effects, just like for example "almost" instanton solutions are made relevant in gauge theories with breaking of conformal invariance. Some well motivated modifcations of General Relativity where these singularity problems are absent even at the classical level are discussed. High energy density excitations, responsible for UV divergences in quantum field theories, including quantum gravity, are likely to be the source of child universes which carry them out of the original space time. This decoupling could prevent these high UV excitations from having any influence on physical amplitudes. Child universe production could therefore be responsible for UV regularization in quantum field theories which take into account semiclassically gravitational effects. Child universe production in the last stages of black hole evaporation, the prediction of absence of tranplanckian primordial perturbations, connection to the minimum length hypothesis and in particular the connection to the maximal curvature hypothesis are discussed. Some discussion of superexcited states in the case these states are Kaluza Klein excitations is carried out. Finally, the posibility of obtaining "string like" effects from the wormholes associated with the child universes is discussed.Comment: Talk presented at the IWARA 2009 Conference, Maresias, Brazil, October 2009, accepted for publication in the proceedings, World Scientific format, 8 page

Theorems on gravitational time delay and related issues

Two theorems related to gravitational time delay are proven. Both theorems apply to spacetimes satisfying the null energy condition and the null generic condition. The first theorem states that if the spacetime is null geodesically complete, then given any compact set $K$, there exists another compact set $K'$ such that for any $p,q \not\in K'$, if there exists a ``fastest null geodesic'', $\gamma$, between $p$ and $q$, then $\gamma$ cannot enter $K$. As an application of this theorem, we show that if, in addition, the spacetime is globally hyperbolic with a compact Cauchy surface, then any observer at sufficiently late times cannot have a particle horizon. The second theorem states that if a timelike conformal boundary can be attached to the spacetime such that the spacetime with boundary satisfies strong causality as well as a compactness condition, then any ``fastest null geodesic'' connecting two points on the boundary must lie entirely within the boundary. It follows from this theorem that generic perturbations of anti-de Sitter spacetime always produce a time delay relative to anti-de Sitter spacetime itself.Comment: 15 pages, 1 figure. Example of gauge perturbation changed/corrected. Two footnotes added and one footnote remove

Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds

We refine and extend a programme initiated by one of the current authors [Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the classical energy conditions of general relativity in a cosmological setting to place very general bounds on various cosmological parameters. We show how the energy conditions can be used to bound the Hubble parameter H(z), Omega parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as (relatively) simple functions of the redshift z, present-epoch Hubble parameter H_0, and present-epoch Omega parameter Omega_0. We compare these results with related observations in the literature, and confront the bounds with the recent supernova data.Comment: 21 pages, 2 figure

Wormhole Cosmology and the Horizon Problem

We construct an explicit class of dynamic lorentzian wormholes connecting Friedmann-Robertson-Walker (FRW) spacetimes. These wormholes can allow two-way transmission of signals between spatially separated regions of spacetime and could permit such regions to come into thermal contact. The cosmology of a network of early Universe wormholes is discussed.Comment: 13 pages, in RevTe

Stable gravastars with generalised exteriors

New spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti--de Sitter or de Sitter interior and a Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviours of the equation of state for these parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit

Signature change events: A challenge for quantum gravity?

Within the framework of either Euclidian (functional-integral) quantum gravity or canonical general relativity the signature of the manifold is a priori unconstrained. Furthermore, recent developments in the emergent spacetime programme have led to a physically feasible implementation of signature change events. This suggests that it is time to revisit the sometimes controversial topic of signature change in general relativity. Specifically, we shall focus on the behaviour of a quantum field subjected to a manifold containing regions of different signature. We emphasise that, regardless of the underlying classical theory, there are severe problems associated with any quantum field theory residing on a signature-changing background. (Such as the production of what is naively an infinite number of particles, with an infinite energy density.) From the viewpoint of quantum gravity phenomenology, we discuss possible consequences of an effective Lorentz symmetry breaking scale. To more fully understand the physics of quantum fields exposed to finite regions of Euclidean-signature (Riemannian) geometry, we show its similarities with the quantum barrier penetration problem, and the super-Hubble horizon modes encountered in cosmology. Finally we raise the question as to whether signature change transitions could be fully understood and dynamically generated within (modified) classical general relativity, or whether they require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3: now 24 pages - significantly shortened - argument simplified and more focused - no physics changes - this version accepted for publication in Classical and Quantum Gravit