The non-adiabatic pressure in general scalar field systems

TL;DR

This work analyzes non-adiabatic (entropy) pressure in general scalar-field systems with non-canonical actions $\mathcal L=f(X,\varphi)$ to understand the evolution of the curvature perturbation $\zeta$ on super-horizon scales. It clarifies the distinction between adiabatic sound speed $c_s^2=(\partial P/\partial \rho)_S$ and phase speed $c_{\rm ph}^2$ of perturbations, deriving explicit expressions for both in the general framework and highlighting their different physical roles. The authors show that for a single-field non-canonical model, the non-adiabatic pressure perturbation $\delta P_{\rm nad}$ vanishes on large scales, guaranteeing $\dot{\zeta}=0$ and conservation of the primordial spectrum, while in multi-field cases $\delta P_{\rm nad}$ need not vanish and $\zeta$ can evolve. The results clarify the conditions under which curvature perturbations are conserved and provide a basis for analyzing DBI and other non-canonical inflationary scenarios, with implications for observational constraints on entropy perturbations.

Abstract

We discuss the non-adiabatic or entropy perturbation, which controls the evolution of the curvature perturbation in the uniform density gauge, for a scalar field system minimally coupled to gravity with non-canonical action. We highlight the differences between the sound and the phase speed in these systems, and show that the non-adiabatic pressure perturbation vanishes in the single field case, resulting in the conservation of the curvature perturbation on large scales.