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We study curvature perturbations in the anisotropic inflationary model with a complex scalar field charged
under a $U(1)$ gauge field in Bianchi I universe. Due to Abelian Higgs mechanism, the gauge field acquires
a dynamical mass with an additional longitudinal mode. We verify that the dominant contributions into statistical
anisotropies come from matter fields perturbations and one can neglect the contributions from the metric
perturbations. The contribution of the longitudinal mode in statistical anisotropies power spectrum, though
exponentially small, has an opposite sign compared to the corresponding contribution form the transverse modes.
Since the inflaton field and the transverse modes of the gauge field perturbations have dynamical masses induced
from the symmetry breaking the anisotropy mechanism becomes less efficient. As a result, the observed
constraints on statistical anisotropies can be satisfied with a relaxed fine-tuning on the model parameters such
as the time-dependent gauge kinetic coupling.
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