The purpose of this paper is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon the mathematical structures involved, rather than numerical computations. The opening section reviews and clarifies the Friedmann-Robertson-Walker models of General Relativistic Cosmology, while Section 2 deals with the spatially homogeneous models. Particular attention is...

This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a ‘background-free quantum theory with local degrees of freedom propagating causally’. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensio...

Every finitary monad T on the category of sets is described by an algebraic theory whose n-ary operations are the elements of the free algebra Tn generated by n letters. This canonical presentation of the monad (called its Lawvere theory) offers a precious guideline in the search for an intuitive presentation of the monad by generators and relations. Hence, much work has been devoted to extend ...

We study the cosmology of the Randall-Sundrum brane-world where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. The combined effect of these curvature corrections to the action removes the infinite-density big bang singularity, although the curvature ...

The effect of a time dependent cosmological constant is considered in a family of scalartensor theories. FriedmannRobertsonWalker cosmological models for vacuum and perfect fluid matter are found. They have a linear expansion factor, the so called coasting cosmology, the gravitational ”constant” decreases inversely with time; that is these models satisfy the Dirac Hypotheses. The cosmological ”...

In this paper we apply the dimensional analysis (D.A.) to two cosmological models, Einstein-de Sitter and a Friedmann-RobertsonWalker (FRW) with radiation predominance. We believe that this method is the simplest form to solve the differential equations that present each model and would serve as base to solve more complicated models.

We show how to define a consistent braneworld cosmology in a model in which the brane is constructed as a field-theoretic domain wall of finite thickness. The Friedmann, Robertson-Walker metric is recovered in the region of the brane, but, remarkably, with scale factor that depends on particle energy and on particle species, constituting a breakdown of the weak equivalence principle on sufficie...

We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-BransDicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.

We investigate cosmological solutions of eleven dimensional supergravity compactified on a squashed seven manifold. The effective action for the four dimensional theory contains scalar fields describing the size and squashing of the compactifying space. The potential for these fields consists of a sum of exponential terms. We derive a criterion for an exponential potential to give rise to infla...

We consider a brane generated by a scalar field domain wall configuration in 4+1 dimensions, interpolating, in most cases, between two vacua of the field. We study the cosmology of such a system in the cases where the effective four-dimensional brane metric is de Sitter or anti de Sitter, including a discussion of the bulk coordinate singularities present in the de-Sitter case. We demonstrate t...