George F. R. Ellis

Ideal observational cosmology

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.

A class of homogeneous cosmological models

Einsteins field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector. There are two classes of solutions; these are studied in detail. Three special families of solutions examined include all analytic solutions of the field equations obeying (1) and (2) of which the authors are aware. The relation of these solutions to various vacuum solutions is indicated.

Dynamics of pressure free matter in general relativity

An orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust‐filled space‐time. This is used to study dust‐filled spaces in which there exist multiply transitive groups of motions; all such spaces are classified in detail. Spaces containing shear‐free dust are also considered; it is shown that σ = 0 ⇒ ωΘ = 0. Three classes of solution with σ = 0, ω ≠ 0 are studied. Several new solutions of the field equations are contained in these results.

Universe or multiverse

Bernard Carr and George Ellis present their differing views on whether speculations about other universes are part of legitimate science.

Tilted homogeneous cosmological models

We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.

Singular space-times

A classification scheme for boundary points of incomplete space-times is described. For all classes explicit examples are presented to illustrate the different behaviour of the geometry near those boundary points.

The emergent universe: an explicit construction

We provide a realization of a singularity-free inflationary universe in the form of a simple cosmological model dominated at early times by a single minimally coupled scalar field with a physically based potential. The universe starts asymptotically from an initial Einstein static state, which may be large enough to avoid the quantum gravity regime. It enters an expanding phase that leads to inflation followed by reheating and a standard hot big bang evolution. We discuss the basic characteristics of this emergent model and show that none is at odds with current observations.

Solutions of Einstein's Equations for a Fluid Which Exhibit Local Rotational Symmetry

All solutions of Einsteins equations for pressure‐free matter which exhibit local rotational symmetry were classified in an earlier paper by one of us. This paper extends the earlier theory to the case of a general fluid, with an electromagnetic field possibly present. A classification of these solutions for a perfect fluid is given, and assuming a physically reasonable equation of state, some exact solutions of cosmological interest are obtained. Finally, the difficulties encountered when extending the treatment to a general fluid are discussed; the same general classification can be made.

The geometry of photon surfaces

The photon sphere concept in Schwarzschild space–time is generalized to a definition of a photon surface in an arbitrary space–time. A photon sphere is then defined as an SO(3)×R-invariant photon surface in a static spherically symmetric space–time. It is proved, subject to an energy condition, that a black hole in any such space–time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-invariant photon surface in a general nonstatic spherically symmetric space–time. Many examples are provided.

Time drift of cosmological redshifts as a test of the Copernican principle

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 underdense region around us, purely from background observations.