Perturbative Kähler Moduli Inflation

Abstract: In this work, we present two classes of inflationary models in the framework of type IIB string theory. The inflatons correspond to blow-up K\"ahler modulus arising from compactifying type IIB on a Calabi-Yau. Using perturbative corrections, we first highlight a procedure for stabilising more than one K\"ahler modulus. For the case of two K\"ahler moduli, we explicitly construct two class of inflationary potentials within the K\"ahler cone which satisfy both EFT and cosmological constraints. The first class of models, arising from moduli redefinition of the blow-up mode, have a potential of the form $V(\phi)=V_0(1+C_1 \phi^{2/3})$ align with CMB data with scalar-to-tensor ratio $r\lesssim 10^{-2}$. The second class of models, which have been recently proposed in the name of loop blow-up inflation, have a form $V(\phi)=V_0(1+C_2\phi^{-2/3})$ also agrees with CMB data with scalar-to tensor-ratio $r\lesssim 10^{-8}$.