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

TL;DR

This paper analyzes a ghost-free anisotropic inflation model driven by scalar and vector fields, computing the resulting correlators and their angular dependence, and discusses implications for cosmic microwave background anisotropies.

Contribution

It provides the first detailed calculation of scalar-scalar, scalar-tensor, and tensor-tensor correlators in a specific anisotropic inflation model with a vector field.

Findings

The anisotropy parameter g_* is negative in the simplest model.

Achieving g_* around -0.1 requires the vector energy to be much smaller than the scalar.

Scalar-tensor correlation is smaller than tensor-tensor correlation for typical parameters.

Abstract

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