A new approach to the evolution of cosmological perturbations on large scales

TL;DR

The paper proves that the curvature perturbation on uniform-density hypersurfaces, $\zeta$, remains constant on super-horizon scales for adiabatic perturbations in any gravity theory with local energy-momentum conservation, independent of the gravitational field equations. It derives the evolution equation $\dot{\zeta} = - \frac{H}{\rho+p} \delta p_{\rm nad} - \frac{1}{3} \nabla^2(\sigma+v+B)$ and shows that gradient terms vanish on large scales, tying changes in $\zeta$ to the non-adiabatic pressure, $\delta p_{\rm nad}$. The authors introduce the separate-universe approach, where each super-horizon region evolves as a separate FRW universe, simplifying the tracking of $\zeta$ through inflation (single- and multi-field) and preheating. They discuss implications for isocurvature perturbations and demonstrate how non-adiabatic perturbations in multi-field inflation can drive evolution of $\zeta$, while adiabatic perturbations preserve it. The results extend to non-Einstein theories (e.g., scalar-tensor, brane-world) and provide a robust, physically intuitive framework for connecting early-universe perturbations to late-time cosmology.

Abstract

We discuss the evolution of linear perturbations about a Friedmann-Robertson-Walker background metric, using only the local conservation of energy-momentum. We show that on sufficiently large scales the curvature perturbation on spatial hypersurfaces of uniform-density is conserved when the non-adiabatic pressure perturbation is negligible. This is the first time that this result has been demonstrated independently of the gravitational field equations. A physical picture of long-wavelength perturbations as being composed of separate Robertson-Walker universes gives a simple understanding of the possible evolution of the curvature perturbation, in particular clarifying the conditions under which super-horizon curvature perturbations may vary.

Figures (1)

• Figure 1: A schematic illustration of the separate universes picture, with the symbols as identified in the text.