Over the past decade it has become clear that fundamental strings are not the only fundamental degrees of freedom in string theory. D-branes are also part of the spectrum of fundamental states. In this paper we explore some possible effects of D-branes on early Universe string cosmology, starting with two key assumptions: firstly that the initial state of the Universe corresponded to a dense, hot gas in which all degrees of freedom were in thermal equilibrium, and secondly that the topology of the background space admits one-cycles. We argue by t duality that in this context the cosmological singularities are not present. We derive the equation of state of the brane gases and apply the results to suggest that, in an expanding background, the winding modes of fundamental strings will play the most important role at late times. In particular, we argue that the string winding modes will only allow four space-time dimensions to become large. The presence of brane winding modes with $p>\mathrm{}1\mathrm{}$ may lead to a hierarchy in the sizes of the extra dimensions.

• Received 16 June 2000

DOI:https://doi.org/10.1103/PhysRevD.62.103509