Primordial Anisotropies in Gauged Hybrid Inflation

We study primordial anisotropies generated in the model of gauged hybrid inflation in which the complex waterfall field is charged under a $U(1)$ gauge field. Primordial anisotropies are generated either actively during inflation or from inhomogeneities modulating the surface of end of inflation during waterfall transition. We present a consistent $\delta N$ mechanism to calculate the anisotropic power spectrum and bispectrum. We show that the primordial anisotropies generated at the surface of end of inflation do not depend on the number of e-folds and therefore do not produce dangerously large anisotropies associated with the IR modes. Furthermore, one can find the parameter space that the anisotropies generated from the surface of end of inflation cancel the anisotropies generated during inflation, therefore relaxing the constrains on model parameters imposed from IR anisotropies. We also show that the gauge field fluctuations induce a red-tilted power spectrum so the averaged power spectrum from the gauge field can change the total power spectrum from blue to red. Therefore, hybrid inflation, once gauged under a $U(1)$ field, can be consistent with the cosmological observations.