  The predictions for all the cosmological observables of any inflationary
model depend on the number of e-foldings which is sensitive to the
post-inflationary history of the universe. In string models the generic
presence of light moduli leads to a late-time period of matter domination which
lowers the required number of e-foldings and, in turn, modifies the exact
predictions of any inflationary model. In this paper we compute exactly the
shift of the number of e-foldings in Kaehler moduli inflation which is
determined by the magnitude of the moduli initial displacement caused by vacuum
misalignment and the moduli decay rates. We find that the preferred number of
e-foldings gets reduced from 50 to 45, causing a modification of the spectral
index at the percent level. Our results illustrate the importance of
understanding the full post-inflationary evolution of the universe in order to
derive precise predictions in string inflation. To perform this task it is
crucial to work in a setting where there is good control over moduli
stabilisation.
