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 $$T_1$$ and $$T_2$$ which transform non-trivially under $$U(1)_X$$, and some pairs of fundamental quarks charged under the $$SU(N)\times U(1)_X$$ gauge group. The non-trivial transformations of moduli under $$U(1)_X$$ lead to a moduli-dependent Fayet–Iliopoulos (FI) term. The modulus $$T_2$$ and the real component of $$T_1$$ 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 $$T_1$$ while keeping its axionic part light. Choosing the proper parameters, we obtain a global Minkowski vacuum where the imaginary part of $$T_1$$ has a quadratic potential for chaotic inflation