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) x 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.
