arXiv subjects

John D. Barrow

Publications and source records attributed to John D. Barrow.

At least 73 records · Page 4Linked to original sources

arXiv2015

New Singularities in Unexpected Places

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and impacts upon the end of inflation in the early universe.

gr-qc↗

arXiv2015

Singular Inflation

We prove that a homogeneous and isotropic universe containing a scalar field with a power-law potential, $V(ϕ)=Aϕ^{n}$, with $0 0$ always develops a finite-time singularity at which the Hubble rate and its first derivative are finite, but its second derivative diverges. These are the first examples of cosmological models with realistic matter sources that possess weak singularities of 'sudden' type. We also show that a large class of models with even weaker singularities exist for non-integer $n>1$. More precisely, if $k<n<k+1$ where $k$ is a positive integer then the first divergence of the Hubble rate occurs with its ($k+2)$th derivative. At early times these models behave like standard large-field inflation models but they encounter a singular end-state when inflation ends. We term this singular inflation.

gr-qc↗

arXiv2015

Local Varying-Alpha Theories

In a recent paper we demonstrated how the simplest model for varying alpha may be interpreted as the effect of a dielectric material, generalized to be consistent with Lorentz invariance. Unlike normal dielectrics, such a medium cannot change the speed of light, and its dynamics obey a Klein-Gordon equation. This work immediately suggests an extension of the standard theory, even if we require compliance with Lorentz invariance. Instead of a wave equation, the dynamics may satisfy a local algebraic relation involving the permittivity and the properties of the electromagnetic field, in analogy with more conventional dielectric (but still preserving Lorentz invariance). We develop the formalism for such theories and investigate some phenomenological implications. The problem of the divergence of the classical self-energy can be solved, or at least softened, in this framework. Some interesting new cosmological solutions for the very early universe are found, including the possibility of a bounce, inflation and expansion with a loitering phase, all of which are induced by early variations in alpha.

gr-qc↗

arXiv2014

Maximum Tension: with and without a cosmological constant

We discuss various examples and ramifications of the conjecture that there exists a maximum force (or tension) in general relativistic systems. We contrast this situation with that in Newtonian gravity, where no maximum force exists, and relate it to the existence of natural units defined by constants of Nature and the fact that the Planck units of force and power do not depend on Planck's constant. We discuss how these results change in higher dimensions where the Planck units of force are no longer non-quantum. We discuss the changes that might occur to the conjecture if a positive cosmological constant exists and derive a maximum force bound using the Kottler-Schwarzschild-de Sitter black hole.

gr-qc↗

arXiv2014

Redshifting of cosmological black bodies in BSBM varying-alpha theories

We analyse the behaviour of black-body radiation in theories of electromagnetism which allow the electron charge and the fine structure constant to vary in space and time. We show that such theories can be expressed as relativistic generalizations of a conventional dielectric. By making the appropriate definition of the vector potential and associated gauge transformations, we can identify the equivalent of the electric and displacement fields, $\mathbf{E}$ and $\mathbf{D}$, as well as the magnetic $ \mathbf{B}$ and $\mathbf{H}$ fields. We study the impact of such dielectrics on the propagation of light in the so-called BSBM theory and conclude that no changes are created to the standard cosmological evolution of the temperature and energy-density of black-body radiation.

gr-qc↗

arXiv2014

Limits on a Gravitational Field Dependence of the Proton--Electron Mass Ratio from H$_2$ in White Dwarf Stars

Spectra of molecular hydrogen (H$_2$) are employed to search for a possible proton-to-electron mass ratio ($μ$) dependence on gravity. The Lyman transitions of H$_2$, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions ($T \sim 13\,000$ K) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual H$_2$ transitions shift due to $μ$-dependence. The spectrum of white dwarf star GD133 yields a $Δμ/μ$ constraint of $(-2.7\pm4.7_{\rm stat}\pm 0.2_{\rm sys})\times10^{-5}$ for a local environment of a gravitational potential $ϕ\sim10^4\ ϕ_\textrm{Earth}$, while that of G29$-$38 yields $Δμ/μ=(-5.8\pm3.8_{\rm stat}\pm 0.3_{\rm sys})\times10^{-5}$ for a potential of $2 \times 10^4$ $ϕ_\textrm{Earth}$.

gr-qc↗

arXiv2014

Cosmology: the search for twenty-four (or more) functions

We enumerate the 4(1+F)+2S independent arbitrary functions of space require to describe a general relativistic cosmology containing an arbitrary number of non-interacting fluid (F) and scalar fields (S). Results are also given for arbitrary space dimension and for higher-order gravity theories, where the number increases to 16+4F+2S. Both counts are subject to assumptions about whether the dark energy is a cosmological constant. A more detailed analysis is provided when global homogeneity is assumed and the functions become constants. This situation is also studied in the case where the flat and open universes have compact spatial topologies. This changes the relative generalities significantly and places new constraints on the types of expansion anisotropy that are permitted. The most general compact homogeneous universes containing Friedmann models are spatially flat and described by 8+4F+2S constants. Comparisons are made with the simple 6-parameter lambda-CDM model and physical interpretations provided for the parameters needed to describe the most general cosmological models.

gr-qc↗

arXiv2014

Observational constraints on dual intermediate inflation

We explore the observational implications of models of intermediate inflation driven by modified dispersion relations, specifically those representing the phenomenon of dimensional reduction in the ultraviolet limit. These models are distinct from the standard ones because they do not require violations of the strong energy condition, and this is reflected in their structure formation properties. We find that they can naturally accommodate deviations from exact scale-invariance. They also make clear predictions for the running of the spectral index and tensor modes, rendering the models straightforwardly falsifiable. We discuss the observational prospects for these models and the implications these may have for quantum gravity scenarios.

astro-ph.CO↗

arXiv2013

Inflationary Instabilities of Einstein-Aether Cosmology

We examine the consequences of Lorentz violation during slow-roll inflation. We consider a canonical scalar inflaton coupled, through its potential, to the divergence of a fixed-norm timelike vector field, or "aether." The vector is described by Einstein-aether theory, a vector-tensor model of gravitational Lorentz violation. We derive and analyze the cosmological perturbation equations for the metric, inflaton, and aether. If the scale of Lorentz violation is sufficiently small compared to the Planck mass, and the strength of the scalar-aether coupling is suitably large, then the spin-0 and spin-1 perturbations grow exponentially and spoil the inflationary background. The effects of such a coupling on the CMB are too small to be visible to current or near-future CMB experiments; unusually, no isocurvature modes are produced at first order in a perturbative expansion around the aether norm. These results are discussed for both a general potential and a worked example, $m^2 ϕ^2$ inflation with a quadratic scalar-aether coupling term.

astro-ph.CO↗

arXiv2013

General Dynamics of Varying-Alpha Universes

We introduce and study extensions of the varying alpha theory of Bekenstein-Sandvik-Barrow-Magueijo to allow for an arbitrary coupling function and self-interaction potential term in the theory. We study the full evolution equations without assuming that variations in alpha have a negligible effect on the expansion scale factor and the matter density evolution, as was assumed in earlier studies. The background FRW cosmology of this model in the cases of zero and non-zero spatial curvature is studied in detail, using dynamical systems techniques, for a wide class of potentials and coupling functions. All the asymptotic behaviours are found, together with some new solutions. We study the cases where the electromagnetic parameter, zeta, is positive and negative, corresponding to magnetic and electrostatic energy domination in the non-relativistic matter. In particular, we investigate the cases where the scalar field driving alpha variations has exponential and power-law self-interaction potentials and the behaviour of theories where the coupling constant between matter and alpha variations is no longer a constant.

gr-qc↗

arXiv2013

Intermediate inflation from rainbow gravity

It is possible to dualize theories based on deformed dispersion relations and Einstein gravity so as to map them into theories with trivial dispersion relations and rainbow gravity. This often leads to "dual inflation" without the usual breaking of the strong energy condition. We identify the dispersion relations in the original frame which map into "intermediate" inflationary models. These turn out to be particularly simple: power-laws modulated by powers of a logarithm. The fluctuations predicted by these scenarios are near, but not exactly scale-invariant, with a red running spectral index. These dispersion relations deserve further study within the context of quantum gravity and the phenomenon of dimensional reduction in the ultraviolet.

astro-ph.CO↗

arXiv2013

Geodesics at Sudden Singularities

We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for isotropic and homogeneous universes. Further discussion of the weakness of the singularity is also included.

gr-qc↗

arXiv2013

Limits on the dependence of the fine-structure constant on gravitational potential from white-dwarf spectra

We propose a new probe of the dependence of the fine structure constant, alpha, on a strong gravitational field using metal lines in the spectra of white dwarf stars. Comparison of laboratory spectra with far-UV astronomical spectra from the white dwarf star G191-B2B recorded by the Hubble Space Telescope Imaging Spectrograph gives limits on the fractional variation of alpha of (Delta alpha/alpha)=(4.2 +- 1.6)x10^(-5) and (-6.1 +- 5.8)x10^(-5) from Fe V and Ni V spectra, respectively, at a dimensionless gravitational potential relative to Earth of (Delta phi) ~ 5x10^(-5). With better determinations of the laboratory wavelengths of the lines employed these results could be improved by up to two orders of magnitude.

astro-ph.CO↗

arXiv2013

Bouncing Anisotropic Universes with Varying Constants

We examine the evolution of a closed, homogeneous and anisotropic cosmology subject to a variation of the fine structure 'constant', α, within the context of the theory introduced by Bekenstein, Sandvik, Barrow and Magueijo, which generalises Maxwell's equations and general relativity. The variation of αpermits an effective ghost scalar field, whose negative energy density becomes dominant at small length scales, leading to a bouncing cosmology. A thermodynamically motivated coupling which describes energy exchange between the effective ghost field and the radiation field leads to an expanding, isotropizing sequence of bounces. In the absence of entropy production we also find solutions with stable anisotropic oscillations around a static universe.

gr-qc↗

arXiv2013

Cosmologies in Horndeski's second-order vector-tensor theory

Horndeski derived a most general vector-tensor theory in which the vector field respects the gauge symmetry and the resulting dynamical equations are of second order. The action contains only one free parameter, $λ$, that determines the strength of the non-minimal coupling between the gauge field and gravity. We investigate the cosmological consequences of this action and discuss observational constraints. For $λ<0$ we identify singularities where the deceleration parameter diverges within a finite proper time. This effectively rules out any sensible cosmological application of the theory for a negative non-minimal coupling. We also find a range of parameter that gives a viable cosmology and study the phenomenology for this case. Observational constraints on the value of the coupling are rather weak since the interaction is higher-order in space-time curvature.

gr-qc↗

arXiv2013

Series expansions and sudden singularities

We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with a sudden singularity containing two free constants, as required for a general solution of the cosmological equations.

gr-qc↗

arXiv2012

The Instabilities of Bianchi Type IX Einstein Static Universes

We investigate the stability of the Einstein static universe as a non-LRS Bianchi type IX solution of the Einstein equations in the presence of both non-tilted and tilted fluids. We find that the static universe is unstable to homogeneous perturbations of Bianchi type IX to the future and the past.

gr-qc↗

arXiv2012

Some Inflationary Einstein-Aether Cosmologies

We show how to derive several families of accelerating universe solutions to an Einstein-Aether gravity theory. These solutions provide possible descriptions of inflationary behaviour in the early universe and late-time cosmological acceleration.

gr-qc↗