\bf $\delta M$ Formalism and Anisotropic Chaotic Inflation Power Spectrum

Abstract

A new analytical approach to linear perturbations in anisotropic inflation has been introduced in [A. Talebian-Ashkezari, N. Ahmadi and A.A. Abolhasanib, JCAP 03(2018)001] under the name of $\delta M$ formalism. In this paper we apply the mentioned approach to a model of anisotropic inflation driven by a scalar field, coupled to the kinetic term of a vector field with a $U(1)$ symmetry. The $\delta M$ formalism provides an efficient way of computing tensor- tensor, tensor- scalar as well as scalar- scalar 2-point correlations that are needed for the analysis of the observational features of an anisotropic model on the CMB. A comparison between $\delta M$ results and the tedious calculations using in-in formalism shows the aptitude of the $\delta M$ formalism in calculating accurate two point correlation functions between physical modes of the system.