William R. Stoeger
University of Arizona
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Physics Reports | 1985
George F. R. Ellis; S.D. Nel; R. Maartens; William R. Stoeger; A.P. Whitman
Abstract Following Kristian and Sachs direct observational approach to cosmology, this paper analyses in detail the information that can be obtained from idealised astronomical observations, firstly in the cosmographic case when no gravitational field equations are assumed, and secondly in the cosmological case when Einsteins field equations of General Relativity are taken to determine the space-time structure. It is shown that if ideal observations are available, in the cosmographic case they are insufficient to determine the space-time structure on the past light cone of the observer; however in the cosmological case they are precisely necessary and sufficient to determine the space-time geometry on the light cone and in its causal past (at least down to where caustics or curps first occur). The restricted case of spherically symmetric space-times is analysed in detail, and necessary and sufficient observational conditions that such a space-time be spatially homogeneous are proven. A subsequent paper will examine the situation of realistic observational data.
Physical Review D | 1995
R. Maartens; George F. R. Ellis; William R. Stoeger
We consider directly the equations by which matter imposes anisotropies on freely propagating background radiation, leading to a new way of using anisotropy measurements to limit the deviations of the Universe from a Friedmann-Robertson-Walker (FRW) geometry. This approach is complementary to the usual Sachs-Wolfe approach: the limits obtained are not as detailed, but they are more model independent. We also give new results about combined matter-radiation perturbations in an almost-FRW universe, and a new exact solution of the linearized equations.
The Astrophysical Journal | 1997
William R. Stoeger; Marcelo E. Araujo; Tim Gebbie
Assuming that the cosmological principle holds, Maartens, Ellis, & Stoeger (MES) recently constructed a detailed scheme linking anisotropies in the cosmic background radiation (CMB) with anisotropies and inhomogeneities in the large-scale structure of the universe and showed how to place limits on those anisotropies and inhomogeneities simply by using CMB quadrupole and octupole limits. First, we indicate and discuss the connection between the covariant multiple moments of the temperature anisotropy used in the MES scheme and the quadrupole and octupole results from COBE. Then we introduce those results into the MES limit equations to obtain definite quantitative limits on the complete set of cosmological measures of anisotropy and inhomogeneity. We find that all the anisotropy measures are less than 10-4 in the case of those not affected by the expansion rate H and less than 10-6 Mpc-1 in the case of those which are. These results demonstrate quantitatively that the observable universe is indeed close to Friedmann-Lemaitre-Robertson-Walker (FLRW) on the largest scales and can be modeled adequately by an almost-FLRW model—that is, the anisotropies and inhomogeneities characterizing the observable universe on the largest scales are not too large to be considered perturbations to FLRW.
Classical and Quantum Gravity | 1992
William R. Stoeger; George F. R. Ellis; S D Nel
The authors give the exact spherically symmetric solution of the Einstein field equations for dust (p=0) in observational coordinates for data on the past light cone C-(p0) consisting of redshifts, observer area distances, and galaxy number counts. A Bondi potential is found, which facilitates the integration. Also they show in detail how FLRW models can be constructed via these solutions from FLRW data. Finally, they discuss their approach with respect to other observationally oriented treatments, particularly those of Ehlers and Rindler (1987), and Rindler and Suson (1989).
The Astrophysical Journal | 2003
Marcelo B. Ribeiro; William R. Stoeger
This paper aims to connect the theory of relativistic cosmology number counts with the astronomical data, practice, and theory behind the galaxy luminosity function (LF). We treat galaxies as the building blocks of the universe but ignore most aspects of their internal structures by considering them as point sources. However, we do consider general morphological types in order to use data from galaxy redshift surveys, where some kind of morphological classification is adopted. We start with a general relativistic treatment for a general spacetime, not just for Friedmann-Lemaitre-Robertson-Walker, of number counts, and then we link the derived expressions with the LF definition adopted in observational cosmology. Then equations for differential number counts, the related relativistic density per source, and observed and total relativistic energy densities of the universe, as well as other related quantities, are written in terms of the luminosity and selection functions. As an example of how these theoretical/observational relationships can be used, we apply them to test the LF parameters determined from the CNOC2 galaxy redshift survey, for consistency with the Einstein-de Sitter (EdS) cosmology, which they assume, for intermediate redshifts. We conclude that there is a general consistency for the tests we carried out, namely, for both the observed relativistic mass-energy density and the observed relativistic mass-energy density per source, which is equivalent to differential number counts, in an EdS universe. In addition, we find clear evidence of a large amount of hidden mass, as has been obvious from many earlier investigations. At the same time, we find that the CNOC2 LF gives differential galaxy counts somewhat above the EdS predictions, indicating that this survey observes more galaxies at 0.1 z 0.4 than the models predictions.
Classical and Quantum Gravity | 1996
Roy Maartens; Neil P. Humphreys; David R. Matravers; William R. Stoeger
Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observers galactic worldline. The field equations are reduced to a single first-order ODE in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. FRW), but at larger redshift develops an inhomogeneity. New observational characterizations of homogeneity (FRW universes) are also given.
The Astrophysical Journal | 2007
Vinicius Albani; Alvaro Iribarrem; Marcelo B. Ribeiro; William R. Stoeger
This paper uses data obtained from the galaxy luminosity function (LF) to calculate two types of radial number density statistics of the galaxy distribution as discussed in Ribeiro, namely, the differential density γ and the integral differential density γ*. By applying the theory advanced by Ribeiro & Stoeger, which connects the relativistic cosmology number counts with the astronomically derived LF, the differential number counts dN/dz are extracted from the LF and used to calculate both γ and γ* with various cosmological distance definitions, namely, area distance, luminosity distance, galaxy area distance, and redshift distance. LF data are taken from the CNOC2 galaxy redshift survey, and γ and γ* are calculated for two cosmological models: Einstein-de Sitter and an Ω = 0.3, Ω = 0.7 standard cosmology. The results confirm the strong dependency of both statistics on the distance definition, as predicted in Ribeiro, as well as showing that plots of γ and γ* against the luminosity and redshift distances indicate that the CNOC2 galaxy distribution follows a power-law pattern for redshifts higher than 0.1. These findings support Ribeiros theoretical proposition that using different cosmological distance measures in statistical analyses of galaxy surveys can lead to significant ambiguity in drawing conclusions about the behavior of the observed large-scale distribution of galaxies.
Classical and Quantum Gravity | 1992
William R. Stoeger; S J Stanley; D Nel; George F. R. Ellis
For pt.IV see ibid., vol.9, p.1711, (1992). The authors set up and solve the general (no symmetries assumed) first-order equations for dust (p=0) relative to an FLRW background in observational coordinates using the fluid-ray (FR) tetrad formalism, with data on the past light cone C-(p0) consisting of galaxy redshifts, observer area distances, galaxy number counts and null shear measures. Cosmological proper motions are not needed in the data set. A detailed framework for constructing solutions from any such data set is given, although no concrete solutions are presented. The character of these solutions will depend heavily on the data themselves.
Classical and Quantum Gravity | 1992
William R. Stoeger; S D Nel; R Maartens; George F. R. Ellis
The authors describe the fluid-ray (FR) tetrad, which is based on the four-velocity u of the cosmological fluid and the null vector k which lies along the generators of the null geodesics in the past light cones C-(p0) centred on the worldline C. Then, they formulate the field equations in terms of this tetrad, giving also the Jacobi identities, the metric variable equations for observational coordinates, and the contracted Bianchi identities. The equivalent set of equations, involving the Ricci identities, the full Bianchi identities, along with the contracted Bianchi identities, is also given. This formulation facilitates the integration of the field equations in certain cosmological contexts.
Monthly Notices of the Royal Astronomical Society | 2009
George F. R. Ellis; William R. Stoeger
The causal limit usually considered in cosmology is the particle horizon, delimiting the possibilities of causal connection in the expanding Universe. However, it is not a realistic indicator of the effective local limits of important interactions in space–time. We consider here the matter horizon for the Solar system, i.e. the comoving region which has significantly contributed matter to our local physical environment. This lies inside the effective domain of dependence, which (assuming the universe is dominated by dark matter along with baryonic matter and vacuum-energy-like dark energy) consists of those regions that have had a significant active physical influence on this environment through effects such as matter accretion and acoustic waves. It is not determined by the velocity of light c, but by the flow of matter perturbations along their world lines and associated gravitational effects. We emphasize how small a region the perturbations which became our Galaxy occupied, relative to the observable universe – even relative to the smallest scale perturbations detectable in the cosmic microwave background radiation. Finally, looking to the future of our local cosmic domain, we suggest simple dynamical criteria for determining the present domain of influence and the future matter horizon. The former is the radial distance at which our local region is just now separating from the cosmic expansion. The latter represents the limits of growth of the matter horizon in the far future.