# Effective field theory of statistical anisotropies for primordial bispectrum and gravitational waves

## TL;DR

This paper develops an effective field theory framework to analyze primordial statistical anisotropies in inflation, focusing on their impact on scalar and tensor perturbations and their correlations.

## Contribution

It introduces a comprehensive EFT approach to quantify anisotropies in scalar and tensor spectra, including their bispectrum and cross correlations, in models with non-trivial gauge field dynamics.

## Key findings

- Derived expressions for anisotropies in scalar power spectrum and bispectrum.
- Calculated statistical anisotropy in tensor power spectrum.
- Analyzed scalar-tensor cross correlations in anisotropic inflation models.

## Abstract

We present the effective field theory studies of primordial statistical anisotropies in models of anisotropic inflation. The general action in unitary gauge is presented to calculate the leading interactions between the gauge field fluctuations, the curvature perturbations and the tensor perturbations. The anisotropies in scalar power spectrum and bispectrum are calculated and the dependence of these anisotropies to EFT couplings are presented. In addition, we calculate the statistical anisotropy in tensor power spectrum and the scalar-tensor cross correlation. Our EFT approach incorporates anisotropies generated in models with non-trivial speed for the gauge field fluctuations and sound speed for scalar perturbations such as in DBI inflation.