Moduli evolution in the presence of flux compactifications

We study the cosmological evolution of the volume moduli in a class of recently proposed Inflationary Universe models arising out of Type IIB string theory, where a number of the moduli fields have been stabilised through flux compactifications. Developing an approach initially introduced in [3] we show, in agreement with [4], how the presence of extra sources of matter act so as to provide additional friction, slowing the modulus field as it evolves down its potential, thereby vastly increasing the region of parameter space which leads to the eventual stabilisation of these fields. Extending the case to include both the real and imaginary parts of the volume modulus, we show how the parameter space of inital conditions is modified and comment on the impact for these inflationary models arising out of flux type compactifications.