Conserved cosmological perturbation in Galileon models

TL;DR

The paper establishes the existence of a fully nonlinear conserved curvature perturbation on super-Hubble scales in Galileon-type scalar-field models using two complementary methods. First, it shows that the Galileon fluid becomes perfect and barotropic on large scales via energy-momentum conservation, yielding adiabatic perturbations; second, it derives a fully nonlinear, non-perturbative action for the curvature perturbation $\zeta$ demonstrating that $\zeta =\text{const}$ is an exact large-scale solution. The key result is that higher-derivative braiding effects are suppressed on large scales, so the Galileon field effectively behaves like a $k$-essence field for curvature perturbations, with a 2-2 mapping $\rho(\phi,\dot{\phi})$, $P(\phi,\dot{\phi})$ ensuring barotropy. This conservation provides a robust link between primordial perturbations and late-time cosmology in both the $G(X,\phi)\Box\phi$ case and the generalized Galileon, with broad implications for early-universe model-building and observational predictions.

Abstract

We prove the existence of a fully nonlinear conserved curvature perturbation on large scales in Galileon-type scalar field models in two approaches. The first approach is based on the conservation of energy-momentum tensor of the Galileon field, which is also the familiar approach in understanding the conservation in $k$-essence or perfect fluid models. We show that the fluid corresponding to the Galileon field becomes perfect and barotropic on large scales, which is responsible to the conservation. The difference from $k$-essence model is that, besides the energy-momentum conservation, the Einstein equation must be employed in order to complete the proof of barotropy. In the second approach, we derive the fully non-perturbative action for the curvature perturbation $ζ$ in Galileon model on large scales, and argue that $ζ=const$ is indeed an exact solution on large scales. This conservation of curvature perturbation is important since it relates the later and the primordial universe.