Using cosmology to constrain the topology of hidden dimensions

Abstract

A four-dimensional universe, arising from a flux compactification of Type IIB string theory, contains scalar fields with a potential determined by topological and geometric parameters of the internal -hidden- dimensions. We show that inflation can be realized via rolling towards the large internal volume minima that are generic in these scenarios, and we give explicit formulae relating the microscopic parameters (e.g., the Euler number of the internal space) to the cosmological observables (e.g., the spectral index). We find that the tensor-to-scalar ratio, the running of the spectral index, and the potential energy density at the minimum are related by consistency relations and are exponentially small in the number of e-foldings. Further, requiring that these models arise as low-energy limits of string theory eliminates most of them, even if they are phenomenologically valid. In this context, this approach provides a strategy for systematically falsifying stringy inflation models.