# Cosmological implications of shift symmetric Galileon field

## TL;DR

This paper constructs a ghost-free covariant Galileon model with internal shift symmetry, showing it cannot alone explain late-time acceleration unless the symmetry is weakly broken to include a potential.

## Contribution

It provides a new ghost-free, shift-symmetric covariant Galileon formulation applicable to all interaction terms, and explores how breaking the symmetry enables late-time acceleration.

## Key findings

- Pure shift-symmetric Galileon cannot predict late-time acceleration.
- Weak symmetry breaking allows potential inclusion, explaining acceleration.
- The model remains ghost-free and internally consistent.

## Abstract

A ghost-free metric formulation of the recently proposed covariant Galileon model \cite{RPgal} which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileon Lagrangian, allows us to include an appropriate potential term which can explain late time acceleration, in accordance with recent findings in the literature.