# Anisotropic inflation in Brans-Dicke gravity

## TL;DR

This paper investigates anisotropic inflation within Brans-Dicke gravity, demonstrating how anisotropy evolves and depends on model parameters through numerical analysis, with implications for CMB observations.

## Contribution

It introduces a detailed numerical study of anisotropic inflation in Brans-Dicke gravity, highlighting the dependence of anisotropy on key parameters and its behavior as an attractor.

## Key findings

- Anisotropy is proportional to the slow-roll parameter.
- Anisotropy grows with the number of e-folds.
- Higher Brans-Dicke parameter and coupling constant suppress anisotropy.

## Abstract

We study anisotropic inflation in the Brans-Dicke gravity in the presence of an abelian gauge field where the gauge field is non-minimally coupled to the inflaton. We show that the degree of anisotropy, under slow-roll approximations, is proportional to slow roll parameter of the theory. As demonstration, we consider the displaced quadratic potential for the inflation. We do the numerical calculation of the model to investigate the behavior of anisotropy by changing the parameter in the Brans-Dicke model. We find out that, the solution is an attractor in the phase space, and anisotropy grows with number of e-folds. Anisotropy depends on Brans-Dicke parameter, $ \omega $, initial values of the scalar field and constant parameter of the coupling function of the scalar field and the abelian gauge field, $ c $. If we consider upper bound on the number of e-folds from CMB i.e. $ 60 $ e-folds, by increasing $ \omega $ and $ c $, anisotropy do not have time to exit the horizon and suppressed.