On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy

This version deposited at arxiv 02-10-12 arXiv:1210.0730v1. Subsequently published in Physical Review D as Phys. Rev. D 87, 063517 (2013) http://link.aps.org/doi/10.1103/PhysRevD.87.063517. Copyright American Physical Society (APS).11 pages11 pages11 pages11 pagesThe problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes

Dynamics of a lattice Universe

We find a solution to Einstein field equations for a regular toroidal lattice of size L with equal masses M at the centre of each cell; this solution is exact at order M/L. Such a solution is convenient to study the dynamics of an assembly of galaxy-like objects. We find that the solution is expanding (or contracting) in exactly the same way as the solution of a Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average density as our model. This points towards the absence of backreaction in a Universe filled with an infinite number of objects, and this validates the fluid approximation, as far as dynamics is concerned, and at the level of approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum Gravit

High-energy Emission from Pulsar Outer Magnetospheres

We investigate a stationary pair production cascade in the outer magnetosphere of an isolated, spinning neutron star. The charge depletion due to global flows of charged particles, causes a large electric field along the magnetic field lines. Migratory electrons and/or positrons are accelerated by this field to radiate gamma-rays via curvature and inverse-Compton processes. Some of such gamma-rays collide with the X-rays to materialize as pairs in the gap. The replenished charges partially screen the electric field, which is self-consistently solved together with the energy distribution of particles and gamma-rays at each point along the field lines. By solving the set of Maxwell and Boltzmann equations, we demonstrate that an external injection of charged particles at nearly Goldreich-Julian rate does not quench the gap but shifts its position and that the particle energy distribution cannot be described by a power-law. The injected particles are accelerated in the gap and escape from it with large Lorentz factors. We show that such escaping particles migrating outside of the gap contribute significantly to the gamma-ray luminosity for young pulsars and that the soft gamma-ray spectrum between 100 MeV and 3 GeV observed for the Vela pulsar can be explained by this component. We also discuss that the luminosity of the gamma-rays emitted by the escaping particles is naturally proportional to the square root of the spin-down luminosity.Comment: 24 pages, 11 figures; to appear in the inaugural (Sep) issue of Progress in Astrophysics Researches (a new book series

Push-pull fatigue properties of wires in an iridium - 5% tungsten alloy

Introduction This memorandum reports a series of tests to determine the fatigue properties of an iridium - 5% tungsten alloy at 600°c and 700°C. A previous memorandum, Memo. Mat. 61, reports the fatigue properties at room temperature of the same alloy

Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape

We consider the cosmological dynamics associated with volume weighted measures of eternal inflation, in the Bousso-Polchinski model of the string theory landscape. We find that this measure predicts that observers are most likely to find themselves in low energy vacua with one flux considerably larger than the rest. Furthermore, it allows for a satisfactory anthropic explanation of the cosmological constant problem by producing a smooth, and approximately constant, distribution of potentially observable values of Lambda. The low energy vacua selected by this measure are often short lived. If we require anthropically acceptable vacua to have a minimum life-time of 10 billion years, then for reasonable parameters a typical observer should expect their vacuum to have a life-time of approximately 12 billion years. This prediction is model dependent, but may point toward a solution to the coincidence problem of cosmology.Comment: 35 pages, 8 figure

Cosmological solutions with charged black holes

RB aknowledges support from the Higher Education Commission (HEC) of Pakistan, which provided funding to visit QMUL while this work was performed. TC and JD are supported by the STFC

Exact Evolution of Discrete Relativistic Cosmological Models

22 pages, 16 figures22 pages, 16 figuresWe study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions

Constraints on the Variation of G from Primordial Nucleosynthesis

We study here the effect of a varying G on the evolution of the early Universe and, in particular, on primordial nucleosynthesis. This variation of G is modelled using the Brans-Dicke theory as well as a more general class of scalar-tensor theories. Modified nucleosynthesis codes are used to investigate this effect and the results obtained are used to constrain the parameters of the theories. We extend previous studies of primordial nucleosynthesis in scalar-tensor theories by including effects which can cause a slow variation of G during radiation domination and by including a late-time accelerating phase to the Universe's history. We include a brief discussion on the epoch of matter-radiation equality in Brans-Dicke theory, which is also of interest for determining the positions of the cosmic microwave background power-spectrum peaks.Comment: 10 pages, 7 figures. Published versio

Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.Comment: 17 pages, to appear in Class. Quant. Gra

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and