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We study the cosmological implications of an effective field theory modelderived within a configuration of D7 brane stacks in the framework of type-IIBstring theory. We consider a suitable geometric setup where the K\"ahler modulifields are stabilised and the parametric space is constrained so that a deSitter vacuum is ensured. In addition to the moduli fields we also take intoaccount the usual Higgs and matter fields included in the effective fieldtheory. In this background we implement the standard hybrid inflation scenariowith a singlet scalar field acting as the inflaton and the Higgs states servingas waterfall fields. Radiative corrections and soft supersymmetry breakingterms play an essential role in the realisation of a successful inflationaryscenario consistent with the present cosmological data. Small tensor-to-scalarratio values are predicted, which can be probed in future planned experiments.Further constraints on the model's parameters are derived from bounds on darkradiation, which is measured as a contribution to the effective number ofneutrino species $N_{eff}$. In particular, we find an excess of $\DeltaN_{eff}\leq{0.95}$ at $2\sigma$ confidence level with natural values of theinvolved couplings.

Moduli Stabilisation, de Sitter Vacua and Hybrid Inflation in Large Volume Compactifications