Papers by David L Wiltshire
Average homogeneity is only reached on scales greater than 70–100h−1Mpc yet standard peculiar vel... more Average homogeneity is only reached on scales greater than 70–100h−1Mpc yet standard peculiar velocity approaches assume an most Euclidean geometry below this scale. Furthermore, the Friedmann equation is applied in the nonlinear regime, although this has no motivation in the fundamental principles of general relativity. We investigate the variance of the Hubble expansion in a manner which makes no prior geometrical assumptions, other than the existence of a suitably averaged linear Hubble law. We use the COMPOSITE data set of 4534 galaxies [Watkins, Feldman and Hudson (2009)].
Journal of Cosmology and Astroparticle Physics
We develop methods for investigating baryon acoustic oscillation (BAO) features in cosmological m... more We develop methods for investigating baryon acoustic oscillation (BAO) features in cosmological models with non-trivial (but slowly varying) averaged spatial curvature: models that are not necessarily flat, close to flat, nor with constant spatial curvature. The class of models to which our methods apply include Lemaître-Tolman-Bondi models, modified gravity cosmologies, and inhomogeneous cosmologies with backreaction-in which we do not have a prediction of the shape of the spatial 2-point correlation function, but where we nevertheless expect to see a BAO feature in the present-day galaxy distribution, in form of an excess in the galaxy 2-point correlation function. We apply our methods to the Baryon Oscillation Spectroscopic Survey (BOSS) dataset, investigating both the Lambda Cold Dark Matter (ΛCDM) and timescape cosmological models as case studies. The correlation functions measured in the two fiducial models contain a similarly-pronounced BAO feature. We use the relative tangential and radial BAO scales to measure the anisotropic Alcock-Paczyński distortion parameter, , which is independent of the underlying BAO preferred scale. We find that is consistent with zero in both fiducial cosmologies, indicating that models with a different spatial curvature evolution can account for the relative positions of the tangential and radial BAO scale. We validate our methods using ΛCDM mocks.
Physica Scripta, 2017
General relativity is a set of physical and geometric principles, which lead to a set of (Einstei... more General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of particles on the background. But open questions remain, including: What is the scale on which matter and geometry are dynamically coupled in the Einstein equations? Are the field equations valid on small and large scales? What is the largest scale on which matter can be coarse grained while following a geodesic of a solution to Einstein's equations? We address these questions. If the field equations are causal evolution equations, whose average on cosmological scales is not an exact solution of the Einstein equations, then some simplifying physical principle is required to explain the statistical homogeneity of the late epoch Universe. Such a principle may have its origin in the dynamical coupling between matter and geometry at the quantum level in the early Universe. This possibility is hinted at by diverse approaches to quantum gravity which find a dynamical reduction to two effective dimensions at high energies on one hand, and by cosmological observations which are beginning to strongly restrict the class of viable inflationary phenomenologies on the other. We suggest that the foundational principles of general relativity will play a central role in reformulating the theory of spacetime structure to meet the challenges of cosmology in the 21st century.
Physical Review D, 2012
In this first paper we present a Lagrangian framework for the description of structure formation ... more In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a general-relativistic analogue of Zel'dovich's approximation for the description of structure formation in cosmology, and compare it with previous suggestions in the literature. This approximation is then investigated: paraphrasing the derivation in the Newtonian framework we provide general-relativistic analogues of the basic system of equations for a single dynamical field variable and recall the first-order perturbation solution of these equations. We then define a general-relativistic analogue of Zel'dovich's approximation and investigate its implications by functionally evaluating relevant variables, and we address the singularity problem. We so obtain a possibly powerful model that, although constructed through extrapolation of a perturbative solution, can be used to put into practice nonperturbatively, e.g. problems of structure formation, backreaction problems, nonlinear properties of gravitational radiation, and light-propagation in realistic inhomogeneous universe models. With this model we also provide the key-building blocks for initializing a fully relativistic numerical simulation.
Monthly Notices of the Royal Astronomical Society
Parameters that quantify the acceleration of cosmic expansion are conventionally determined withi... more Parameters that quantify the acceleration of cosmic expansion are conventionally determined within the standard Friedmann-Lemaître-Robertson-Walker (FLRW) model, which fixes spatial curvature to be homogeneous. Generic averages of Einstein's equations in inhomogeneous cosmology lead to models with non-rigidly evolving average spatial curvature, and different parametrizations of apparent cosmic acceleration. The timescape cosmology is a viable example of such a model without dark energy. Using the largest available supernova data set, the JLA catalogue, we find that the timescape model fits the luminosity distance-redshift data with a likelihood that is statistically indistinguishable from the standard spatially flat Λ cold dark matter cosmology by Bayesian comparison. In the timescape case cosmic acceleration is nonzero but has a marginal amplitude, with best-fitting apparent deceleration parameter, q 0 = −0.043 +0.004 −0.000. Systematic issues regarding standardization of supernova light curves are analysed. Cuts of data at the statistical homogeneity scale affect light curve parameter fits independent of cosmology. A cosmological model dependence of empirical changes to the mean colour parameter is also found. Irrespective of which model ultimately fits better, we argue that as a competitive model with a non-FLRW expansion history, the timescape model may prove a useful diagnostic tool for disentangling selection effects and astrophysical systematics from the underlying expansion history.
Journal of Cosmology and Astroparticle Physics
We investigate-in a generic setting-the regime of applicability of the Alcock
Astronomy & Astrophysics
Saulder et al. (2019, A&A, 622, A83) have performed a novel observational test of the local expan... more Saulder et al. (2019, A&A, 622, A83) have performed a novel observational test of the local expansion of the Universe for the standard cosmology as compared to an alternative model with differential cosmic expansion. Their analysis employs mock galaxy samples from the Millennium Simulation, a Newtonian N–body simulation on a ΛCDM background. For the differential expansion case the simulation has been deformed in an attempt to incorporate features of a particular inhomogeneous cosmology: the timescape model. It is shown that key geometrical features of the timescape cosmology have been omitted in this rescaling. Consequently, the differential expansion model tested by Saulder et al. (2019) cannot be considered to approximate the timescape cosmology.
Journal of Cosmology and Astroparticle Physics
The Universe on scales 10-100 h −1 Mpc is dominated by a cosmic web of voids, filaments, sheets a... more The Universe on scales 10-100 h −1 Mpc is dominated by a cosmic web of voids, filaments, sheets and knots of galaxy clusters. These structures participate differently in the global expansion of the Universe: from non-expanding clusters to the above average expansion rate of voids. In this paper we characterize Hubble expansion anisotropies in the COMPOSITE sample of 4534 galaxies and clusters. We concentrate on the dipole and quadrupole in the rest frame of the Local Group. These both have statistically significant amplitudes. These anisotropies, and their redshift dependence, cannot be explained solely by a boost of the Local Group in the Friedmann-Lemaître-Robertson-Walker (FLRW) model which expands isotropically in the rest frame of the cosmic microwave background (CMB) radiation. We simulate the local expansion of the Universe with inhomogeneous Szekeres solutions, which match the standard FLRW model on > ∼ 100 h −1 Mpc scales but exhibit nonkinematic relativistic differential expansion on small scales. We restrict models to be consistent with observed CMB temperature anisotropies, while simultaneously fitting the redshift variation of the Hubble expansion dipole. We include features to account for both the Local Void and the "Great Attractor". While this naturally accounts for the Hubble expansion and CMB dipoles, the simulated quadrupoles are smaller than observed. Further refinement to incorporate additional structures may improve this. This would enable a test of the hypothesis that some large angle CMB anomalies result from failing to treat the relativistic differential expansion of the background geometry; a natural feature of solutions to Einstein's equations not included in the current standard model of cosmology.
Classical and Quantum Gravity, Jul 1, 1989
Page 1. Spherically symmetric solutions in dimensionally reduced spacetimes This article has been... more Page 1. Spherically symmetric solutions in dimensionally reduced spacetimes This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1989 Class. ... Printed in the UK Spherically symmetric solutions in dimensionally reduced spacetimes ...
These lecture notes review the theoretical problems associated with coarse-graining the observed ... more These lecture notes review the theoretical problems associated with coarse-graining the observed inhomogeneous structure of the universe at late epochs, of describing average cosmic evolution in the presence of growing inhomogeneity, and of relating average quantities to physical observables. In particular, a detailed discussion of the timescape scenario is presented. In this scenario, dark energy is realized as a misidentification of gravitational energy gradients which result from gradients in the kinetic energy of expansion of space, in the presence of density and spatial curvature gradients that grow large with the growth of structure. The phenomenology and observational tests of the timescape model are discussed in detail, with updated constraints from Planck satellite data. In addition, recent results on the variation of the Hubble expansion on < 100/h Mpc scales are discussed. The spherically averaged Hubble law is significantly more uniform in the rest frame of the Local Group of galaxies than in the conventional rest frame assumed for the Cosmic Microwave Background. This unexpected result supports a fundamental revision of the notion of the cosmic rest frame, consistent with the expectations of the timescape scenario.
This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience w... more This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A brief history of quantum cosmology. 2. Hamiltonian formulation of general relativity: 2.1 The 3+1 decomposition; 2.2 The action. 3. Quantisation: 3.1 Superspace; 3.2 Canonical quantisation; 3.3 Path integral quantisation; 3.4 Minisuperspace; 3.5 The WKB approximation; 3.6 Probability measures; 3.7 Minisuperspace for the Friedmann universe with massive scalar field. 4. Boundary Conditions: 4.1 The no-boundary proposal; 4.2 The tunneling proposal. 5. The predictions of quantum cosmology: 5.1 The period of inflation; 5.2 The origin of density perturbations; 5.3 The arrow of time.
Below scales of about 100/h Mpc our universe displays a complex inhomogeneous structure dominated... more Below scales of about 100/h Mpc our universe displays a complex inhomogeneous structure dominated by voids, with clusters of galaxies in sheets and filaments. The coincidence that cosmic expansion appears to start accelerating at the epoch when such structures form has prompted a number of researchers to question whether dark energy is a signature of a failure of the standard cosmology to properly account, on average, for the distribution of matter we observe. Here I discuss the timescape scenario, in which cosmic acceleration is understood as an apparent effect, due to gravitational energy gradients that grow when spatial curvature gradients become significant with the nonlinear growth of cosmic structure. This affects the calibration of local geometry to the solutions of the volume--average evolution equations corrected by backreaction. I further discuss recent work on defining observational tests for average geometric quantities which can distinguish the timescape model from a co...
Dark Matter in Astrophysics and Particle Physics - Proceedings of the 7th International Heidelberg Conference on Dark 2009, 2010
I discuss potential observational tests of a "radically conservative" solution to the p... more I discuss potential observational tests of a "radically conservative" solution to the problem of dark energy in cosmology, in which the apparent acceleration of the universe is understood as a consequence of gravitational energy gradients that grow when spatial curvature gradients become significant with the nonlinear growth of cosmic structure. In particular, I discuss measures equivalent to the dark energy equation of state, baryon acoustic oscillation statistic DV, H(z), the Om(z) diagnostic, an average inhomogeneity diagnostic, and the time-drift of cosmological redshifts.
Physics Letters B, 1987
It is shown that the extension of the spacetime supersymmetric Green-Schwarz covariant superstrin... more It is shown that the extension of the spacetime supersymmetric Green-Schwarz covariant superstring action to p-dimensional extended objects (pbranes) is possible if and only if the on-shell p-dimensional bose and fermi degrees of freedom are equal. This is further evidence for world-tube supersymmetry in these models. All the p-brane models are related to superstring actions in d = 3, 4, 6 or 10 dimensions by double dimensional reduction, (which we generalise to reduction on arbitrary compact spaces), and we also show how they may be considered as topological defects of supergravity theories.
Physics Letters B, 1986
The low energy expansion of supersymmetric string theory suggests that the leading correction to ... more The low energy expansion of supersymmetric string theory suggests that the leading correction to the Einstein action is given by the Gauss-Bonnet invariant. A generalisation of Birkhoff's theorem in the case of Einstein-Maxwell theory modified by a Gauss-Bonnet term is proved. The only spherically symmetric solutions of the theory are shov, n to he generalisations of the Reissner-Nordstrom and Robinson-Bertotti solutions. The "'Reissncr-Nordstrom'" solutions have asymptotically flat and asymptotically anti-de Sitter branches, however, the latter are unstable.
Physical Review D, 1987
The qualitative theory of dynamical systems is used to present an analysis of the phase space of ... more The qualitative theory of dynamical systems is used to present an analysis of the phase space of Kaluza-Klein cosmological solutions with even-dimensional internal space, an arbitrary cosmological constant, and Freund-Rubin compactification. If either the physical or internal manifold has a single spatial dimension the cosmological solutions may correspond to black-hole interiors and pathological behavior can be expected. It is shown that such behavior does not occur in general, however. Some solutions with dilatons are also discussed.
Physical Review D, 1988
Spherically symmetric solutions of d-dimensional Einstein-Maxwell theory with a Gauss-Bonnet term... more Spherically symmetric solutions of d-dimensional Einstein-Maxwell theory with a Gauss-Bonnet term are classified. All spherically "yim^tri nolutions of d-dimensional Einstein gravity coupled to the fiaurs-flonnct and Borri-InTeld terms are derived, classified and comnared wit. 1 tiip revious solutions. Thermodynamic properties of the black lio]f*r. 'i-c discussed and the black hole temperatures derived. Unlike the r.u'! .nt i on:; the Kinstei n-Mnxwr] I theory the solutions with a Born-Trc'V": d term do li^t nrvear f .o inive n r.tnhle endpoint with regard to thermal evaporation. MIRAMAHE-THIE5TE Mtirrii ]O88 i I t."il ft;s-until i rat) 0:1.
Journal of Physics A: Mathematical and General, 1986
ABSTRACT The algebra of the restricted Lorentz group and the Weyl formulation of massless Poincar... more ABSTRACT The algebra of the restricted Lorentz group and the Weyl formulation of massless Poincare irreducible fields have been developed by primarily Lorentz-covariant Pauli matrix methods which facilitate the generation of both indexed Weyl spinor identities and Dirac identities. The results have been used to display a complex set of symmetries for the (anti)self-dual Weyl field strengths of arbitrary helicity j(&gt;or=1). These symmetries and the requirement of Poincare irreducibility have then been used to give a direct and uniform determination of the forms of the gauge invariant (Lagrangian) free field wave equations for the Fierz-Pauli and Rarita-Schwinger potentials of spin 1, 3/2 and 2. The procedures set out indicate that it should be possible to establish the gauge invariant Lagrangian free field wave equations of arbitrary helicity in a uniform and direct manner from the corresponding much simpler equations governing the field strengths in unmixed spin representations.
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Papers by David L Wiltshire