# John D. Barrow - DAMTP, UK

## Contact Details

NameJohn D. Barrow |
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AffiliationDAMTP, UK |
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CityCambridge |
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CountryUnited Kingdom |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesGeneral Relativity and Quantum Cosmology (47) Cosmology and Nongalactic Astrophysics (44) High Energy Physics - Theory (28) High Energy Physics - Phenomenology (10) Physics - History of Physics (3) Physics - Atomic Physics (2) High Energy Astrophysical Phenomena (1) |

## Publications Authored By John D. Barrow

We investigate the behaviour of bouncing Bianchi type IX `Mixmaster' universes in general relativity. This generalises all previous studies of the cyclic behaviour of closed spatially homogeneous universes with and without entropy increase. We determine the behaviour of models containing radiation by analytic and numerical integration and show that increase of radiation entropy leads to increasing cycle size and duration. Read More

Hot white dwarf stars are the ideal probe for a relationship between the fine-structure constant and strong gravitational fields, providing us with an opportunity for a direct observational test. We study a sample of hot white dwarf stars, combining far-UV spectroscopic observations, atomic physics, atmospheric modelling and fundamental physics, in the search for variation in the fine structure constant. This variation manifests as shifts in the observed wavelengths of absorption lines, such as quadruply ionized iron (FeV) and quadruply ionized nickel (NiV), when compared to laboratory wavelengths. Read More

Conjectures play a central role in theoretical physics, especially those that assert an upper bound to some dimensionless ratio of physical quantities. In this paper we introduce a new such conjecture bounding the ratio of the magnetic moment to angular momentum in nature. We also discuss the current status of some old bounds on dimensionless and dimensional quantities in arbitrary spatial dimension. Read More

We analyse the kinematics of cosmological spacetimes with nonzero torsion, in the framework of the classical Einstein-Cartan gravity. After a brief introduction to the basic features of spaces with non-vanishing torsion, we consider a family of observers moving along timelike worldlines and focus on their kinematic behaviour. In so doing, we isolate the irreducible variables monitoring the observers' motion and derive their evolution formulae and associated constraint equations. Read More

We use a new mathematical approach to reconstruct the equation of state and the inflationary potential for the inflaton field from the spectral indices for the density perturbations $n_{s}$ and the tensor to scalar ratio $r$. According to the astronomical data, the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that $n_{s}-1=h\left( r\right) $. Read More

In the context of generalised Brans-Dicke cosmology we use the Killing tensors of the minisuperspace in order to determine the unspecified potential of a scalar-tensor gravity theory. Specifically, based on the existence of contact symmetries of the field equations, we find four types of potentials which provide exactly integrable dynamical systems. We investigate the dynamical properties of these potentials by using a critical point analysis and we find solutions which lead to cosmic acceleration and under specific conditions we can have de-Sitter points as stable late-time attractors. Read More

In a homogeneous and isotropic universe with non-zero spatial curvature we consider the effects of gravitational particle production in the dynamics of the universe. We show that the dynamics of the universe in such a background are characterized by a single nonlinear differential equation which is significantly dependent on the rate of particle creation and whose solutions can be dominated by curvature effects at early times. For different particle creation rates we apply the singularity test in order to find the analytic solutions of the background dynamics. Read More

An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. Read More

In the cosmological scenario in $f\left( T\right) $ gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we apply is that of movable singularities of differential equations. For the isotropic universe, the solutions are expressed in terms of a Laurent expansion, while for the anisotropic universe we find a family of exact Kasner-like solutions in vacuum. Read More

We investigate how a Higgs mechanism could be responsible for the emergence of gravity in extensions of Einstein theory. In this scenario, at high energies, symmetry restoration could "turn off" gravity, with dramatic implications for cosmology and quantum gravity. The sense in which gravity is muted depends on the details of the implementation. Read More

We consider the application of group invariant transformations in order to constrain a flat isotropic and homogeneous cosmological model, containing of a Brans-Dicke scalar field and a perfect fluid with a constant equation of state parameter $w$, where the latter is not interacting with the scalar field in the gravitational action integral. The requirement that the Wheeler-DeWitt equation be invariant under one-parameter point transformations provides us with two families of power-law potentials for the Brans-Dicke field, in which the powers are functions of the Brans-Dicke parameter $\omega_{BD}$ and the parameter $w$. The existence of the Lie symmetry in the Wheeler-DeWitt equation is equivalent to the existence of a conserved quantity in field equations and with oscillatory terms in the wavefunction of the universe. Read More

We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropisation on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialise to consider the closed Bianchi type IX universe and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. Read More

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. Read More

**Affiliations:**

^{1}RCAAM: Academy of Athens,

^{2}DAMTP: University of Cambridge

Rubano and Barrow have discussed the emergence of a dark energy, with late-time cosmic acceleration arising from a self-interacting homogeneous scalar field with a potential of hyperbolic power type. Here, we study the evolution of this scalar field potential back in the inflationary era. Using the hyperbolic power potential in the framework of inflation, we find that the main slow-roll parameters, like the scalar spectral index, the running of the spectral index and the tensor-to-scalar fluctuation ratio can be computed analytically. Read More

We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for investigation. We show how simple counting arguments can be used to characterise parts of the general solution of Einstein's equations when various matter fields are present and with different spatial topologies. Read More

We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the existence of a point transformation under which the WdW equation is invariant is equivalent to the existence of conservation laws for the field equations, which indicates the existence of analytical solutions. Read More

We prove that a homogeneous and isotropic universe containing a scalar field
with a power-law potential, $V(\phi )=A\phi ^{n}$, with $0

In his 2005 review, Gravity and the Thermodynamics of Horizons, Paddy suggested that a vacuum in thermal equilibrium with a bath of radiation should have a gradually diminishing energy. We work through the consequences of this scenario, and find that a coupling between the vacuum and a bath of black-body radiation at the temperature of the horizon requires the Hubble rate, $H$, to approach the same type of evolution as in the "intermediate inflation" scenario, with $H\propto t^{-1/3}$, rather than as a constant. We show that such behaviour does not conflict with observations when the vacuum energy is described by a slowly-rolling scalar field, and when the fluctuations in the scalar field are treated as in the "warm inflation" scenario. Read More

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. Read More

**Authors:**Julija Bagdonaite

^{1}, Edcel J. Salumbides

^{2}, Simon P. Preval

^{3}, Martin A. Barstow

^{4}, John D. Barrow

^{5}, Michael T. Murphy

^{6}, Wim Ubachs

^{7}

**Affiliations:**

^{1}VU University Amsterdam, Netherlands,

^{2}VU University Amsterdam, Netherlands,

^{3}University of Leicester, UK,

^{4}University of Leicester, UK,

^{5}DAMTP, UK,

^{6}Swinburne University of Technology, Australia,

^{7}VU University Amsterdam, Netherlands

Spectra of molecular hydrogen (H$_2$) are employed to search for a possible proton-to-electron mass ratio ($\mu$) 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 $\mu$-dependence. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

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. Read More

We examine the evolution of a closed, homogeneous and anisotropic cosmology subject to a variation of the fine structure 'constant', \alpha, within the context of the theory introduced by Bekenstein, Sandvik, Barrow and Magueijo, which generalises Maxwell's equations and general relativity. The variation of \alpha permits 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. Read More

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. Read More

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, $\lambda$, 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. Read More

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. Read More

General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum effects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar fields in an isotropic and homogeneous background leading to future singularities. Read More

In this paper, we formulate a generalization of the simple Bekenstein-Sandvik-Barrow-Magueijo (BSBM) theory of varying alpha by allowing the coupling constant, \omega, for the corresponding scalar field \psi\ to depend on \psi. We focus on the situation where \omega\ is exponential in \psi\ and find the late-time behaviours that occur in matter-dominated and dark-energy dominated cosmologies. We also consider the situation when the background expansion scale factor of the universe evolves in proportion to an arbitrary power of the cosmic time. Read More

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. Read More

We make the cosmological constant, {\Lambda}, into a field and restrict the variations of the action with respect to it by causality. This creates an additional Einstein constraint equation. It restricts the solutions of the standard Einstein equations and is the requirement that the cosmological wave function possess a classical limit. Read More

In this work we study the cosmology of the general f(T) gravity theory. We express the modified Einstein equations using covariant quantities, and derive the gauge-invariant perturbation equations in covariant form. We consider a specific choice of f(T), designed to explain the observed late-time accelerating cosmic expansion without including an exotic dark energy component. Read More

It is widely believed that primordial magnetic fields are dramatically diluted by the expansion of the universe. As a result, cosmological magnetic fields with residual strengths of astrophysical relevance are generally sought by going outside standard cosmology, or by extending conventional electromagnetic theory. Nevertheless, the survival of strong B-fields of primordial origin is possible in spatially open Friedmann universes without changing conventional electromagnetism. Read More

We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. Read More

We present a new solution to the cosmological constant (CC) and coincidence problems in which the observed value of the CC, $\Lambda$, is linked to other observable properties of the universe. This is achieved by promoting the CC from a parameter which must to specified, to a field which can take many possible values. The observed value of Lambda ~ 1/(9. Read More

A coupling between a scalar field (representing the dark energy) and dark matter could produce rich phenomena in cosmology. It affects cosmic structure formation mainly through the fifth force, a velocity-dependent force that acts parallel to particle's direction of motion and proportional to its speed, an effective rescaling of the particle masses, and a modified background expansion rate. In many cases these effects entangle and it is difficult to see which is the dominant one. Read More

We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Read More

We have studied the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) model for the spatial and temporal variations of the fine structure constant, alpha, with the aid of full N-body simulations which explicitly and self-consistently solve for the scalar field driving the alpha-evolution. We focus on the scalar field (or equivalently alpha) inside the dark matter halos and find that the profile of the scalar field is essentially independent of the BSBM model parameter. This means that given the density profile of an isolated halo and the background value of the scalar field, we can accurately determine the scalar field perturbation in that halo. Read More

We introduce the N-body simulation technique to follow structure formation in linear and nonlinear regimes for the extended quintessence models (scalar-tensor theories in which the scalar field has a self-interaction potential and behaves as dark energy), and apply it to a class of models specified by an inverse power-law potential and a non-minimal coupling. Our full solution of the scalar field perturbation confirms that, when the potential is not too nonlinear, the effects of the scalar field could be accurately approximated as a modification of background expansion rate plus a rescaling of the effective gravitational constant relevant for structure growth. For the models we consider, these have opposite effects, leading to a weak net effect in the linear perturbation regime. Read More

We extend the usual gravitational action principle by promoting the bare cosmological constant (CC) from a parameter to a field which can take many possible values. Variation leads to a new integral constraint equation which determines the classical value of the effective CC that dominates the wave function of the universe. In a realistic cosmological model, the expected value of the effective CC, is calculated from measurable quantities to be O(t_U), as observed, where t_U is the present age of the universe in Planck units,. Read More

We describe in detail the general methodology and numerical implementation of consistent N-body simulations for coupled scalar field cosmological models, including the background cosmology and the generation of initial conditions (with the different couplings to different matter species taken into account). We perform fully consistent simulations for a class of coupled scalar field models with an inverse power-law potential and negative coupling constant, for which the chameleon mechanism does not operate. We find that in such cosmological models the scalar-field potential plays a negligible role except in the background expansion, and the fifth force that is produced is proportional to gravity in magnitude, justifying the use of a rescaled gravitational constant G in some earlier N-body simulations of similar models. Read More

We show that the inclusion of simple anisotropic pressures stops the isotropic Friedmann universe being a stable attractor as an initial or final singularity is approached when pressures can exceed the energy density. This shows that the situation with isotropic pressures, studied earlier in the context of cyclic and ekpyrotic cosmologies, is not generic, and Kasner-like behaviour occurs when simple pressure anisotropies are present. We find all the asymptotic behaviours and determine the dynamics when the anisotropic principal pressures are proportional to the density. Read More

Solutions of the Friedmann-Lemaitre cosmological equations of general relativity have been found with finite-time singularities that are everywhere regular, have regular Hubble expansion rate, and obey the strong-energy conditions but possess pressure and acceleration singularities at finite time that are not associated with geodesic incompleteness. We show how these solutions with sudden singularities can be constructed using fractional series methods and find the limiting form of the equation of state on approach to the singularity. Read More

We analyse the constraints obtained from new atomic clock data on the possible time variation of the fine structure `constant' and the electron-proton mass ratio and show how they are strengthened when the seasonal variation of Sun's gravitational field at the Earth's surface is taken into account. Read More