Superstring theory initially proposed that the universe is a 10-dimensional space-time, with the topology of a product manifold Y × M, where Y is a compact 6-dimensional space, and M is the flat, 4-dimensional Minkowski space-time of special relativity. It was suggested that the additional 6 spatial dimensions are not seen or detected because they are of very small diameter. The additional dimensions were said to be 'compactified'.
Whereas general relativistic cosmology proposed a variety of curved 4-dimensional geometries and topologies to represent the entire universe, superstring theory seemed incapable of embracing such cosmological scenarios. Braneworld cosmology attempted to rectify this.
Strings can be open or closed, and it is now proposed that the ends of open strings must be confined to the surfaces of compact p-dimensional submanifolds in the 9-dimensions of space. These submanifolds are called D-branes, or Dirichlet-branes. Braneworld cosmology proposes that our universe may be a 3-dimensional D-brane, (or part of such a brane), sweeping out a 4-dimensional submanifold in the 10-dimensional 'bulk' of space-time, and the bulk may contain many such D-branes. It is even proposed that these D-branes could dynamically interact with each other, perhaps triggering events such as the 'Big Bang' in our universe. So, rather than our universe having 9 spatial dimensions, 6 of which are compactified, it is now suggested that our 3-dimensional spatial universe simply doesn't extend into the extra 6 dimensions. Closed strings, such as gravitons, are not confined to D-branes, but can interact with D-branes. Hence, whilst our universe does not extend into the extra dimensions, it is influenced by those extra dimensions.
As this article in November's Scientific American attests, it is now suggested that the characteristics of the 'inflaton' scalar field, responsible for inflation, the hypothetical period of exponential expansion early in the history of our universe, may be explained, either by some of the scalar fields proposed in relation to dynamical branes, or by the so-called moduli fields used to define the shape and size of the other 6 spatial dimensions.