Four-dimensional Cosmology Research Articles

Dynamical compactification, standard cosmology, and the accelerating universe

A cosmological model based on the Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Friedmann-Robertson-Walker equations of standard four-dimensional cosmology are obtained precisely. The pressure in our universe is an effective pressure expressed in terms of the components of the higher dimensional energy-momentum tensor. In particular, this effective pressure could be negative and might therefore explain the acceleration of our present universe. A special feature of this model is that, for a suitable choice of the parameters of the metric, the higher dimensional gravitational coupling constant could be negative.

Cosmic vorticity on the brane

We study vector perturbations about four-dimensional brane-world cosmologies embedded in a five-dimensional vacuum bulk. Even in the absence of matter perturbations, vector perturbations in the bulk metric can support vector metric perturbations on the brane. We show that during de Sitter inflation on the brane vector perturbations in the bulk obey the same wave equation for a massless five-dimensional field as found for tensor perturbations. However, we present the second-order effective action for vector perturbations and find no normalisable zero-mode in the absence of matter sources. The spectrum of normalisable states is a continuum of massive modes that remain in the vacuum state during inflation.

Dynamics of M-theory cosmology

A complete global analysis of spatially flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non-trivial Ramond-Ramond sector is included. The governing equations are written as a dynamical system. Asymptotically, the form fields are dynamically negligible, but play a crucial role in determining the possible intermediate behavior of the solutions (i.e., the nature of the equilibrium points). The only past-attracting solution (source in the system) may be interpreted in the eleven-dimensional setting in terms of flat space. This source is unstable to the introduction of spatial curvature.

Four-dimensional cosmology from dilaton coupled quantum matter in two dimensions

The reduction of 4D Einstein gravity with $N$ minimal scalars leads to specific 2D dilaton gravity with dilaton coupled scalars. Applying s-wave and large $N$ approximation (where large $N$ quantum contribution due to dilaton itself is taken into account) we study 2D cosmology for CGHS model and for reduced Einstein gravity (in both cases with dilaton coupled scalars). Numerical study shows that in most cases we get 2D singular Universe which may correspond to big bang. Nevertheless, big crunch or non-singular Universes are also possible. For reduced 4D Einstein gravity one can regard the obtained 2D cosmology with time-dependent dilaton as 4D Kantowski-Sacks Universe of singular,non-singular or big crunch type.

Inflation from extra dimensions

A gravity-driven inflation is shown to arise from a simple higher-dimensional universe. In vacuum, the shear of n > 1 contracting dimensions is able to inflate the remaining three spatial dimensions. Said another way, the expansion of the 3-volume is accelerated by the contraction of the n-volume. Upon dimensional reduction, the theory is equivalent to a four-dimensional cosmology with a dynamical Planck mass. A connection can therefore be made to recent examples of inflation powered by a dilaton kinetic energy. Unfortunately, the graceful exit problem encountered in dilaton cosmologies will haunt this cosmology as well.

Singularities in Kaluza-Klein-Friedmann cosmological models.

We consider five-dimensional Kaluza-Klein cosmologies that have three-dimensional spatial sections corresponding to Friedmann (Robertson-Walker) spaces. The extra (flat) dimension can be identified to close it to a circle. We investigate the ``crack-of-doom'' singularity in which the extra dimension goes to zero size, inducing a five-dimensional singularity of which the embedded four-dimensional cosmology has no indication until the singularity. In the Chodos-Detweiler model this crack-of-doom singularity occurs at time =\ensuremath{\infty}, while in a closed Friedmann model like those of Mezzacappa and Matzner, it occurs at a finite time near the maximum of expansion. We present a diagrammatic solution for a range of such models, and show that by appropriate (parameter) choices, the ``crack of doom'' can be avoided both in three-sphere and in three-hyperboloid Kaluza-Klein-Friedmann solutions.