Chaotic inflation in no-scale supergravity with string inspired moduli stabilization

The simple chaotic inflation is highly consistent with the BICEP2 experiment, and no-scale supergravity can be realized naturally in various string compactifications. Thus, we construct a chaotic inflation model in no-scale supergravity inspired from Type IIB string compactification with an anomalous U(1)X gauged symmetry. We introduce two moduli T1 and T2 which transform non-trivially under U(1)X , and some pairs of fundamental quarks charged under the SU(N)×U(1)X gauge group. The non-trivial transformations of moduli under U(1)X lead to a moduli-dependent Fayet–Iliopoulos (FI) term. The modulus T2 and the real component of T1 are stabilized by the non-perturbative effect from quark condensation and the U(1)X D-term. In particular, the stabilization from the anomalous U(1)X D-term with moduli-dependent FI term is crucial for inflation since it gives heavy mass to the real component of the modulus T1 while keeping its axionic part light. Choosing the proper parameters, we obtain a global Minkowski vacuum where the imaginary part of T1 has a quadratic potential for chaotic inflation