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This article reviews, and offers supportive reflections on, the main points of Ernan McMullin's provocative 1998 article, “Cosmic Purpose and the Contingency of Human Evolution,’’ reprinted in this issue of Zygon. In it he addresses the important science-theology issue of how the Creator's purpose and intention to assure the emergence of human beings is consonant with the radical contingency of the evolutionary process. After discussing cosmic and biological evolution and critically summarizing recent solutions to this question by Keith Ward, John Polkinghorne, Arthur Peacocke, Alvin Plantinga, and others, who presuppose in different ways that God is subject to time, McMullin compellingly argues for the traditional position, that God is unconditioned by time, and this enables God to work purposefully through contingency, randomness, and chance just as easily as through law-like regularity.

The present-day Universe appears to be homogeneous on very large scales. Yet when the casual structure of the early Universe is considered, it becomes apparent that the early Universe must have been highly inhomogeneous. The current paradigm attempts to answer this problem by postulating the inflation mechanism However, inflation in order to start requires a homogeneous patch of at least the horizon size. This paper examines if dynamical processes of the early Universe could lead to homogenization. In the past similar studies seem to imply that the set of initial conditions that leads to homogenization is of measure zero. This essay proves contrary: a set of initial conditions for spontaneous homogenization of cosmological models can form a set of non-zero measure., 7 pages. Fifth Award in the 2010 Gravity Research Foundation essay competition

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 spacetime. We consider here the matter horizon for the Solar System, that is,the comoving region which has 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 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., 18 pages and 2 figures

In some well-known scenarios of open-universe eternal inflation, developed by Vilenkin and co-workers, a large number of universes nucleate and thermalize within the eternally inflating mega-universe. According to the proposal, each universe nucleates at a point, and therefore the boundary of the nucleated universe is a space-like surface nearly coincident with the future light cone emanating from the point of nucleation, all points of which have the same proper-time. This leads the authors to conclude that at the proper-time t = t_{nuc} at which any such nucleation occurs, an infinite open universe comes into existence. We point out that this is due entirely to the supposition of the nucleation occurring at a single point, which in light of quantum cosmology seems difficult to support. Even an infinitesimal space-like length at the moment of nucleation gives a rather different result -- the boundary of the nucleating universe evolves in proper-time and becomes infinite only in an infinite time. The alleged infinity is never attained at any finite time., 13 pages and 6 figures

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context, as well as how errors and gaps in the data are propagated together with the genuine perturbations. This will provide guidance for solving, and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone., Comment: Latex 23 pages, no figures, submitted to Astrophysical Journal

In this paper we use the integration scheme for the exact spherically symmetric Einstein field equations in observational coordinates recently developed by Araujo and Stoeger, and input data functions for area distance and galaxy number counts that would be obtained if the universe were exactly represented by nonflat Friedmann-Lemaitre-Robertson-Walker models.

Recently we presented limits on the deviation of the Universe from a Friedmann-Robertson-Walker form, which are implied directly by anisotropies in the cosmic background radiation, without assuming inflationary or other models of evolution. Here we weaken some of our previous assumptions, ensuring that all assumptions are in principle observational, and obtain improved limits.

This paper discusses a connection between the relativistic number counts of cosmological sources and the observed galaxy luminosity function (LF). Observational differential number densities are defined and obtained from published LF data using such connection. We observe a distortion in the observational quantities that increases with higher redshift values as compared to the theoretical predictions. The use of different cosmological distance measures plays a role in such a distortion, Comment: 3 pages, 3 figures. Abridged version of arXiv:1201.5571

For many years now theoretical cosmologists have been building on the rich legacy of Georges Lemaitre’s ideas and accomplishments in mathematically modelling the structure and dynamics of the universe. His recognition and careful demonstration of the viability and attractiveness of expanding models of the universe, along with his seminal idea of the “primeval atom,” which would later be referred to as the Big Bang, are very well known. This has led directly, through other important contributions by Friedmann, Robertson and Walker, to the standard perfectly isotropic and spatially homogeneous (smooth) Friedmann-Lemaitre-Robertson-Walker (FLRW) models of our universe. These are certainly a key part of Lemaitre’s legacy. After reviewing those models, we discuss another very important, but less well-known, contribution to fundamental cosmology, his general spherically symmetric cosmological solutions with pressure and a cosmological constant (vacuum energy, which is a leading candidate for dark energy). These models are generalizations of the FLRW models and, in general, are inhomogeneous. In recent years they have stimulated a great deal of research in the quest for further confirming the standard model, understanding the limitations of its perturbed versions, or possibly replacing it with something more adequate. Their importance for advancing our understanding and modelling of the universe, and the ways in which they are presently being studied and deployed, is described and discussed.

In this paper we show that the mass-energy density of the Universe can be fully determined in terms of the cosmological redshifts, their time drifts and angular-diameter distance (observer area distance). Besides providing an indirect measurement of the mass-energy density of the Universe, we show how one can use the time-drift of the cosmological redshifts as a replacement for the mass-energy density element in the minimally required data set to construct an spherically symmetric Lema\^{\i}tre-Tolman-Bondi (LTB) model for the Universe in observational coordinates., Comment: 17 pages

Through astronomy, physics, cosmology, biology and the other sciences we have come to understand a great deal about nature and our amazing universe. We can sketch their main features in very broad strokes – evolution, relationality, nested levels of organization, complexity and potentiality for life and consciousness, contingency, transience and fragility, and order with some directionality. The universe itself has developed from a very simple, homogeneous system into one of incredible complexity – through the efficacy of the interactions which dominate it, and the emerging, highly differentiated relationships which operate within the macroscopic and microscopic systems and subsystems which form within it. But the universe, life and we ourselves are sources of wonder and inspiration – there is an enormous surplus of understanding, meaning, and significance which is nourished by scientific understanding but transcends it. They present themselves as inexhaustibly rich and deep – ultimately as Mystery. Though scientific rationality encounters limits to its capabilities to probe this Mystery more deeply, its incredible success within its competencies points to and validates our rational and personal quest for understanding and meaning beyond the cosmological limit – through the arts, philosophy, theology and the personal engagement from which they arise.

Over the past ninety years we have come to understand and appreciate the world, the universe which embraces it, and their emergence and development in completely new ways. Thanks to astronomy and physics - particularly to the speciality known as cosmology - we now know that the universe we inhabit began expanding and cooling from an extremely hot and dense, homogeneous, simple state about 13.7 billion years ago. That initial state, often now referred to as the Planck era, was so extreme that our current physics is completely unable to describe it. Space and time as we know them had not yet emerged, and the fundamental forces of gravity, electromagnetism, and the strong and weak nuclear interactions were undoubtedly unified, and thus indistinguishable from one another. Only a thorough and complete quantum description of reality, including space-time and gravity - a quantum cosmology - would be adequate. That is something we do not yet possess, although many people are expending tremendous efforts to develop the components of such a description by exploring superstrings, loop-quantum gravity and non-commutative geometry, as well as exploiting semi-classical approaches to quantizing space-time, gravity and the universe itself.

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH12 with a totally geodesic map fromH12 into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.

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.

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 author intends this chapter as a "trial balloon". The chapter sketches God's action can be described in the world, accepting with critical seriousness both the present and projected knowledge of reality as from the sciences, philosophy and other non-theological disciplines, and the present knowledge of God, his/her relationship with people and world, and his/her activity within it. From revelation, and partially from reason, it is know that God exists, created the universe and all that is in it, reveals him/herself to people, loves and cares for people, continually acts within material creation, particularly now through Jesus and the presence of his spirit-a promise which will be fulfilled only after our deaths. There are a series of unsolved problems related to divine action, which flow from this discussion of the impossibility of adequately articulating or modeling God's direct action towards a creature. Keywords: God's direct action; revelation; scientific knowledge of reality

Not only Einstein’s general ideas about gravity, but also his specific field equation (E) have been excellently confirmed in astronomy. Hence one also applies it to other macroscopic problems (hydrodynamic stellar models) and to quantum gravity. There, however, (E) can only be tested in a tiny region just off the mass shell K2 = 0 of free gravitons. One nevertheless believes (E) to hold even at ‘high energies’ (the popular expression for large, Lorentz‐invariant √|K2|), perhaps for all √|K2| < MPl with Planck’s MPl = (8π GNewton)−1/2. We rather accept (E) only as the infrared limit of a more basic equation (W), which involves Weyl’s conformal curvature tensor. We cannot justify (W) or specify its behavior at low and high K by observations or experiments; only connections with particle theories can help. We thus have examined the effect of gravity on the infrared structure of the electron. As a most striking and firm conclusion, we find the huge M Pl totally irrelevant at high ‘energies’. It merely arises ...

The idea of a multiverse -- an ensemble of universes -- has received increasing attention in cosmology, both as the outcome of the originating process that generated our own universe, and as an explanation for why our universe appears to be fine-tuned for life and consciousness. Here we carefully consider how multiverses should be defined, stressing the distinction between the collection of all possible universes, and ensembles of really existing universes that are essential for an anthropic argument. We show that such realised multiverses are by no means unique. A proper measure on the space of all really existing universes or universe domains is needed, so that probabilities can be calculated, and major problems arise in terms of realised infinities. As an illustration we examine these issues in the case of the set of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universes. Then we briefly summarise scenarios like chaotic inflation, which suggest how ensembles of universe domains may be generated, and point out that the regularities which must underlie any systematic description of truly disjoint multiverses must imply some kind of common generating mechanism. Finally, we discuss the issue of testability, which underlies the question of whether multiverse proposals are really scientific propositions., Comment: 32 pages, 2 figures Completely revised text addressing physics issues more fully and omitting philosophical discussions previously included

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 linearised equations., Comment: 18 pages Latex.

The extent to which individual holes in a cluster of black holes with a mass spectrum can liberate and accrete the resulting material by tidally disrupting stars they encounter, or by capturing stars as binary companions is studied. It is found that the smaller black holes in 'the halo' of such clusters can adequately supply themselves to the level M-dot sub h or greater than 0.0001(M-dot sub h) sub crit, and up to 0.05(M-dot sub h)sub crit for the smallest holes, by tidal disruption, as long as the cluster is embedded in a distribution of stars of relatively high density (not less than 0.1M sub cl/cu pc), and as long as the entire cluster of stars is not too compact (not less than 0.5 pc). Consideration is given to modifications this 'internal' mode of supply introduces in the spectrum emitted by such black hole clusters, and to the current status of their viability as models for AGN and QSOs in light of dynamical studies by Quinlan and Shapiro (1987, 1989).

We briefly discuss the different types of accretion disk models which may be relevant to SS 433, especially in terms of their relation to the regions emitting the strongly red and blue shifted Hα and Hβ lines so peculiarly characteristic of this object. In particular we outline in some detail a subcritical accretion disk associated with the lasing recombination ring model of Ruffini, Fang Li Zhi and their co-workers and describe in a very qualitative way the various thick supercritical disks which may be connected with the formation of relativistic jets in SS 433.

Motivated by the need for stronger observational leverage on the black hole hypothesis and for a more detailed characterization of axisymmetric accretion flows across the marginally stable circular orbit atr{inms}, we develop a general approach for describing the non-Keplerian accretion in the regionr{inH}⩽r⩽ r{in0}, wherer{inH}≡ radius of the event horizon andr{in0}⩾r{inms}. Our procedure possesses many advantages, including easily imposed consistency with the Keplerian model forr>r{in0}, the avoidance ofad hoc boundary conditions atr{inms} and/or atr{inH}, and its application also to accretion in Rosen's bimetric theory, whose spherically symmetric solution has the same qualitative orbital topography as that of general relativity. It becomes apparent, furthermore, that the particular viscosity law chosen in our procedure will have a crucial bearing on the flow in the regionr{inms}

We generalize the Papapetrou equations by deriving propagation equations for the energy-momentum and angular momentum of a test body which has both elementary-particle spin and macroscopic rotation and which is moving in background metric and torsion fields. Our results show that the torsion couples to spin but not to rotation. Thus a rotating test body with no net spin will ignore the torsion and move according to the usual Papapetrou equations. Hence the standard tests of gravity are insensitive to a torsion field. We propose experiments (although still infeasible) to compare the motion of a spin-polarized body with the motion of a rotating body. If the spin and rotation precess differently, the theory of gravity cannot be a metric theory but may be a torsion theory.

We present the essential principles of torsion-detection physics and evaluate several conceivable types of experiments and observations for actually detecting torsion fields, reemphasizing also the evident impossibility of successfully searching for its manifestations among cosmological relics. In particular, a polarized body, with net intrinsic (fundamental-particle) spin, is essential for detecting a torsion field. One which possesses only orbital angular momentum—rotation—or an unpolarized intrinsic spin density will not feel torsion. The fundamental problem in searching for such fields is the extremely small basic unit of the coupling or interaction energy between the torsion field and spin,ɛ≈(8πG′/c 2)(ℏ 2/4). The best way of maximizing the total interaction energy is to increase the spin density of the sourceσ s, and, at the same time the “spin number”S D of the detector.

Following Kristian and Sach's 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 Einstein's 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.

Since Rosen's bimetric theory of gravity provides at present a worthy devil's advocate for the black hole hypothesis, it is important for eventual observational work to elaborate the astrophysical consequences and possibilities peculiar to it. We begin to do this by deriving the orbital topography of the spherically symmetric solution to Rosen's field equations-which is relevant to the behavior of relativistic axisymmetric accretion flows-and calculating predicted accretion disk efficiencies, which can be as much as 2.5 times higher than for a disk in Schwarzschild. Thereafter, a brief treatment of the shortest kinematic time scale and the time dilations for in-falling material is given. Finally we show that Birkhoff's theorem does not hold in Rosen's theory, and, therefore, that genuine gravitational monopole radiation is possible. The energy it carries, however, is not positive definite.

This third paper in the series modeling QSOs and AGNs as clusters of accreting black holes studies the accretion flow within an externally supplied cluster. Significant radiation will be emitted by the cluster core, but the black holes in the outer halo, where the flow is considered spherically symmetric, will not contribute much to the overall luminosity of the source because of their large velocities relative to the infalling gas and therefore their small accretion radii. As a result, the scenario discussed in Paper I will refer to the cluster cores, rather than to entire clusters. This will steepen the high-frequency region of the spectrum unless inverse Compton scattering is effective. In many cases accretion flow in the central part of the cluster will be optically thick to electron scattering, resulting in a spectrum featuring optically thick radiative component in addition to power-law regimes. The fitting of these spectra to QSO and AGN observations is discussed, and application to 3C 273 is worked out as an example.