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We compute the phenomenological signatures of a model (Watanabe et al' 09) ofanisotropic inflation driven by a scalar and a vector field. The action for thevector is U(1) invariant, and the model is free of ghost instabilities. Asuitable coupling of the scalar to the kinetic term of the vector allows for aslow roll evolution of the vector vev, and hence for a prolonged anisotropicexpansion; this provides a counter example to the cosmic no hair conjecture. Wecompute the nonvanishing two point correlation functions between physical modesof the system, and express them in terms of power spectra with angulardependence. The anisotropy parameter g_* for the scalar-scalar spectrum(defined as in the Ackerman et al '07 parametrization) turns out to be negativein the simplest realization of the model, which, therefore, cannot account forthe angular dependence emerged in some analyses of the WMAP data. A g_* oforder -0.1 is achieved when the energy of the vector is about 6-7 orders ofmagnitude smaller than that of the scalar during inflation. For such values ofthe parameters, the scalar-tensor correlation (which is in principle adistinctive signature of anisotropic spaces) is smaller than the tensor-tensorcorrelation.

Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation