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Light from `point sources' such as supernovae is observed with a beam width of order of the sources' size - typically less than 1 AU. Such a beam probes matter and curvature distributions that are very different from coarse-grained representations in N-body simulations or perturbation theory, which are smoothed on scales much larger than 1 AU. The beam typically travels through unclustered dark matter and hydrogen with a mean density much less than the cosmic mean, and through dark matter halos and hydrogen clouds. Using N-body simulations, as well as a Press-Schechter approach, we quantify the density probability distribution as a function of beam width and show that, even for Gpc-length beams of 500 kpc diameter, most lines of sight are significantly under-dense. From this we argue that modelling the probability distribution for AU-diameter beams is absolutely critical. Standard analyses predict a huge variance for such tiny beam sizes, and nonlinear corrections appear to be non-trivial. It is not even clear whether under-dense regions lead to dimming or brightening of sources, owing to the uncertainty in modelling the expansion rate which we show is the dominant contribution. By considering different reasonable approximations which yield very different cosmologies we argue that modelling ultra-narrow beams accurately remains a critical problem for precision cosmology. This could appear as a discordance between angular diameter and luminosity distances when comparing SN observations to BAO or CMB distances.

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

A usual causal requirement on a viable theory of matter is that the speed of sound be at most the speed of light. In view of various recent papers querying this limit, the question is revisited here. We point to various issues confronting theories that violate the usual constraint., Comment: v2: additional discussion on models that appear to have superluminal signal speeds; version to appear in GRG

The Cosmic Blackbody Background Radiation pervades the entire Universe, and so falls into every astrophysical black hole. The blueshift of the infalling photons, measured by a static observer, is infinite at the event horizon. This raises a question as to whether a "firewall" of high energy density may form just outside the horizon, or whether the effect can be attributed exclusively to a singular behavior of the static observer's frame at the horizon. In principle, the presence of such firewall may alter the motion of the infalling matter, influence the black hole evolution, or even invalidate the {\it vacuum} Einstein field equation solution as a realistic approximation for black holes. In this paper we show by means of analytic calculations that all these effects indeed exist, but their magnitude is typically negligibly small, even though the matter stress tensor is divergent in the static frame at $r=2M$. That is not surprising because of the divergent relation of that frame to a freely falling frame as $r \rightarrow 2M$; however it represents a kind of classical analogue for the Black Hole Complementarity principle that has been proposed for quantum effects near a black hole. What is perhaps more surprising is the divergence of the radiation stress tensor for massive particles moving on circular geodesic orbits for values of $r$ approaching $r = 3M$. However such orbits will not occur for infalling matter in realistic accretion discs., 18 pages, 4 figures, accepted for publication in Phys. Rev. D

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect., Comment: 21 pages, 5 ps figures, epsf

This paper considers the nature of apparent horizons for astrophysical black hole situated in a realistic cosmological context. Using semi-tetrad covariant methods we study the local evolutions of the boundaries of the trapped region in the spacetime. For a collapsing massive star immersed in a cosmology with Cosmic Background Radiation (CBR), we show that the initial 2 dimensional marginally trapped surface bifurcates into inner and outer horizons. The inner horizon is timelike while the continuous CBR influx into the black hole makes the outer horizon spacelike. We discuss the possible consequences of these features for Hawking radiation in realistic astrophysical contexts., Comment: 14 pages, 4 figures, Minor corrections in the text, Matches the accepted version in Physical Review D

An astrophysical (cosmological) black hole forming in a cosmological context will be subject to a flux of infalling matter and radiation, which will cause the outer apparent horizon (a marginal trapping surface) to be spacelike \cite{ellisetal14}. As a consequence the radiation emitted close to the apparent horizon no longer arrives at infinity with a diverging redshift. Standard calculations of the emission of Hawking radiation then indicate that no blackbody radiation is emitted to infinity by the black hole in these circumstances, hence there will also then be no black hole evaporation process due to emission of such radiation as long as the matter flux is significant. The essential adiabatic condition (eikonal approximation) for black hole radiation gives a strong limit to the black holes that can emit Hawking radiation. We give the mass range for the black holes that can radiate, according to their cosmological redshift, for the special case of the cosmic blackbody radiation (CBR) influx (which exists everywhere in the universe). At a very late stage of black hole formation when the CBR influx decays away, the black hole horizon becomes first a slowly evolving horizon and then an isolated horizon; at that stage, black hole radiation will start. This study suggests that the primordial black hole evaporation scenario should be revised to take these considerations into account., Comment: To appear, GRG Journal

Cosmology has made enormous progress in the last several decades. It is no longer a neglected subfield of physics, as it was as recently as 1960; it is instead an active area of fundamental research that can boast of a Standard Model well-supported by observations. Prior to 1965 research in cosmology had a strikingly philosophical tone, with debates focusing explicitly on scientific method and the aims and scope of cosmology (see, e.g. Munitz 1962; North 1965; Kragh 1996). One might suspect that with the maturation of the field these questions have been settled, leaving little room for philosophers to contribute. Although the nature of the field has changed dramatically with an increase of observational knowledge and theoretical sophistication, there are still ongoing foundational debates regarding cosmology’s proper aims and methods. Cosmology confronts a number of questions dear to the hearts of philosophers of science: the limits of scientific explanation, the nature of physical laws, and different types of underdetermination, for example. There is an opportunity for philosophers to make fruitful contributions to debates in cosmology and to consider the ramifications of new ideas in cosmology for other areas of philosophy and foundations of physics. Due to the uniqueness of the universe and its inaccessibility, cosmology has often been characterized as “un-scientific” or inherently more speculative than other parts of physics. How can one formulate a scientific theory of the “universe as a whole”? Even those who reject skepticism regarding cosmology often assert instead that cosmology can only make progress by employing a distinctive methodology. These discussions, in my view, have by and large failed to identify the source and the extent of the evidential challenges faced by cosmologists. There are no convincing, general no-go arguments showing the impossibility of secure knowledge in cosmology; there are instead specific problems that arise in attempting to gain observational and theoretical access to the universe. In some cases, cosmologists have achieved knowledge as secure as that in other areas of physics — arguably, for example, in the account of big bang nucleosynthesis. Cosmologists do, however, face a number of distinctive challenges. The finitude of the speed of light, a basic feature of relativistic cosmology, insures that global properties of the universe cannot be established directly by observations (§5). This is a straightforward limit on observational access to the universe, but there are other obstacles of a different kind. Cosmology relies on extrapolating local physical laws to hold universally. These extrapolations make it possible to infer, from observations of standard candles such as Type Ia supernovae,1 the startling conclusion

All spacetimes for an irrotational collisionless fluid with a purely electric Weyl tensor, with spacetime curvature determined by the exact Einstein field equations, are shown to be integrable. These solutions include the relativistic generalisations of the Zeldovich solutions of Newtonian theory. Thus our result shows the consistency of various studies of "silent" universes (where such consistency was assumed rather than proved)., Comment: submitted to Physical Review D, 23 pages, Latex

This paper reviews research in theoretical cosmology in South Africa, providing an overview of the work that has been done and the groups involved in that work.

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.

We present the time drift of the cosmological redshift in a general spherically symmetric spacetime. We demonstrate that its observation would allow us to test the Copernican principle and so determine if our universe is radially inhomogeneous, an important issue in our understanding of dark energy. In particular, when combined with distance data, this extra observable allows one to fully reconstruct the geometry of a spacetime describing a spherically symmetric under-dense region around us, purely from background observations., Comment: 4 pages. Version matching the published text in PRL

A detailed model is presented which explains the observed range 1 ≈γ< 20 of Lorentz factors for superluminal jets. In the model e+e≈ plasma moves in a moderately super Eddington radiation field, L ≈ 10L Edd , of an accretion disk around a black hole. The observed range of γ0 follows from special relativity and from the ratio of proton to electron mass m p /m e = 1836. The results depend only weakly on the details of electromagnetic pre-acceleration of particles close to the black hole. However, the model is consistent only for initial speeds Y in < 108.

Closed, singularity-free, inflationary cosmological models have recently been studied in the context of general relativity. Despite their appeal, these so called emergent models suffer from a number of limitations. These include the fact that they rely on an initial Einstein static state to describe the past eternal phase of the universe. Given the instability of such a state within the context of general relativity, this amounts to a very severe fine tuning. Also in order to be able to study the dynamics of the universe within the context of general relativity, they set the initial conditions for the universe in the classical phase. Here we study the existence and stability of such models in the context of Loop Quantum Cosmology and show that both these limitations can be partially remedied, once semi-classical effects are taken into account. An important consequence of these effects is to give rise to a static solution (not present in GR), which dynamically is a centre equilibrium point and located in the more natural semi-classical regime. This allows the construction of emergent models in which the universe oscillates indefinitely about such an initial static state. We construct an explicit emergent model of this type, in which a non-singular past eternal oscillating universe enters a phase where the symmetry of the oscillations is broken, leading to an emergent inflationary epoch, while satisfying all observational and semi-classical constraints. We also discuss emergent models in which the universe possesses both early- and late-time accelerating phases., Comment: 11 pages, 8 figures

Theories proposing a varying speed of light have recently been widely promoted under the claim that they offer an alternative way of solving the standard cosmological problems. Recent observational hints that the fine structure constant may have varied during over cosmological scales also has given impetus to these models. In theoretical physics the speed of light, $c$, is hidden in almost all equations but with different facets that we try to distinguish. Together with a reminder on scalar-tensor theories of gravity, this sheds some light on these proposed varying speed of light theories., 14 pages, Latex

We present a general framework for analyzing spatially inhomogeneous cosmological dynamics. It employs Hubble-normalized scale-invariant variables which are defined within the orthonormal frame formalism, and leads to the formulation of Einstein's field equations with a perfect fluid matter source as an autonomous system of evolution equations and constraints. This framework incorporates spatially homogeneous dynamics in a natural way as a special case, thereby placing earlier work on spatially homogeneous cosmology in a broader context, and allows us to draw on experience gained in that field using dynamical systems methods. One of our goals is to provide a precise formulation of the approach to the spacelike initial singularity in cosmological models, described heuristically by Belinski\v{\i}, Khalatnikov and Lifshitz. Specifically, we construct an invariant set which we conjecture forms the local past attractor for the evolution equations. We anticipate that this new formulation will provide the basis for proving rigorous theorems concerning the asymptotic behavior of spatially inhomogeneous cosmological models., Comment: 31 pages, 10 *.ps figures, 3 tables, LaTeX2e (10pt), submitted for publication to Physical Review D

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c_{s}^2>1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilise an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed., some additional comments and references; version to appear in Class. Quant. Grav

Cosmology has progressed in the last 35 years from a mainly mathematical and philosophical exercise to an important branch of both astronomy and physics, and is now part of mainstream science, with a well-established standard model confirmed by various strands of evidence (Weinberg 1972; Peebles et al. 1991; Coles and Ellis 1997). Nevertheless because of its nature, it is different from any other branch of the natural sciences. The major issue causing the differences is the uniqueness of its object of study—the Universe as a whole—together with its role as the background for all the rest of physics and science, the resulting problems being accentuated by its vast scale and the extreme energies occurring in the early universe. We are unable to manipulate in any way its originating conditions, and there are limitations on our ability both to observe to very distant regions and very early times and also to test the physics relevant at the earliest times. Consequently it is inevitable that (as is the case for the other historical sciences) specific philosophical choices will to some degree shape the nature of cosmological theory, particularly when it moves beyond the purely descriptive to an explanatory role—which move is central to its impressive progress. These philosophical choices will dominate the resulting understanding to the extent that we pursue a theory with more ambitious explanatory aims.

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 study the peculiar motion of non-relativistic matter in a fully covariant way. The exact nonlinear equations are derived and then applied to the case of pressure-free matter, moving relatively to a quasi-Newtonian Eulerian frame. Our two-frame formalism facilitates the study of the nonlinear kinematics of the matter, as the latter decouples from the background expansion and starts to ``turn around'' and collapse. Applied to second perturbative order, our equations provide a fully covariant formulation of the Zeldovich approximation, which by construction addresses the mildly nonlinear regime of structure formation. Employing a dynamical system approach, we show that, just like in the Newtonian case, the relativistic treatment also predicts that pancakes are the natural end-structures for any generic overdensity., Comment: Minor changes, accepted by Phys. Rev. D

We model massive dark objects in galactic nuclei as spherically symmetric static naked singularities in the Einstein massless scalar field theory and study the resulting gravitational lensing in detail. Based on whether or not a naked singularity is covered within a photon sphere we classify naked singularities into two kinds: weakly naked (those contained within at least one photon sphere) and strongly naked (those not contained within any photon sphere). The qualitative features of gravitational lensing due to a weakly naked singularity are similar to those due to a Schwarzschild black hole (these give rise to one Einstein ring but no radial critical curve). However, the gravitational lensing due to a strongly naked singularity is qualitatively different from that due to a Schwarzschild black hole; a strongly naked singularity gives rise to either two or nil Einstein ring(s) and one radial critical curve. A light ray passing close to a photon sphere of a black hole or a weakly naked singularity goes around its photon sphere once, twice, or many times (before reaching an observer) depending upon the impact parameter and thus gives rise to a sequence of theoretically infinite number of relativistic images, which are highly demagnified. A strongly naked singularity produces no relativistic images.

We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint equations arise to maintain zero shear of the non-comoving fundamental worldlines which define a Newtonian-like frame, and these lead to the (1+3)-covariant dynamical equations, including a generalized Poisson-type equation. We investigate the relation between peculiar velocity and peculiar acceleration, finding the conditions under which they are aligned. In this case we find (1+3)-covariant relativistic generalizations of well-known Newtonian results., Comment: 8 pages, LaTeX2e (iopart); minor changes, matches version accepted for publication by Classical and Quantum Gravity

This is the second of a series of papers extending the 1+3 covariant and gauge invariant treatment of kinetic theory to an examination of Cosmic Microwave Background temperature anisotropies arising from inhomogeneities in the early universe. The first paper dealt with algebraic issues. Here we derive the mode form of the integrated Boltzmann equations, first, giving a covariant version of the standard derivation using the mode recursion relations, second, demonstrating the link to the multipole divergence equations and finally various analytic ways of solving the resulting equations are discussed. A general integral form of solution is obtained for the equations with Thomson scattering. The covariant Friedmann-Lemaitre multipole form of the transport equations are found using the covariant and gauge-invariant generalization of the Peebles and Yu expansion in Thompson scattering time. The dispersion relations and damping scale are then obtained from the covariant approach. The equations are integrated to give the covariant and gauge-invariant equivalent of the canonical scalar sourced anisotropies. We carry out a simple treatment of the matter dominated free-streaming projection, slow decoupling, and tight-coupling cases, with the aim both giving a unified transparent derivation of this range of results and clarifying the connection between the more usual approaches (for example that of Hu and Sugiyama) and the treatment for scalar perturbations (for example the treatment of Challinor and Lasenby)., To appear in Annals of Physics