We find the power-law solutions in (4+n)-dimensional cosmology with time-varying cosmological constant and study the phase of cosmic evolution. The model corresponds to the modification of the higher dimensional vacuum Kasner model. When a dimensionfull parameter in the model takes special value, it is shown that 4-dimensional universe is accelerated expansion. ∗[email protected]

Cosmological consequences of the brane world scenario are reviewed in a pedagogical manner. According to the brane world idea, the standard model particles are confined on a hyper–surface (a so–called brane), which is embedded in a higher– dimensional spacetime (the so–called bulk). We begin our review with the simplest consistent brane world model: a single brane embedded in a five–dimensional...

Recent theoretical developments have generated a strong interest in the “brane-world” picture, which assumes that ordinary matter is trapped in a three-dimensional submanifold, usually called brane, embedded in a higher dimensional space. The purpose of this review is to introduce some basic results concerning gravity in these models and then to present various aspects of the cosmology in a bra...

This is an extended account of a short presentation with this title given at the Minneapolis IMA Workshop on ‘n-categories: foundations and applications’, June 7-18, 2004, organised by John Baez and Peter May.

The theory we describe in this book was developed over a long period, starting about 1965, and always with the aim of developing groupoid methods in homotopy theory of dimension greater than 1. Algebraic work made substantial progress in the early 1970s, in work with Chris Spencer, and in 1974 by Brown and Higgins. A substantial step forward in 1974 led us over the years into many fruitful area...

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

In theories with extra dimensions, the cosmological hierarchy problem can be thought of as unnaturally large radius observable universe in Kaluza-Klein units. We sketch a dynamical mechanism that relaxes this. early scenario we propose, three spatial dimensions arise through tunneling from 'cosmic egg', an effectively one-dimensional configuration all compact and comparable, small size. If stri...