Cosmological Perturbations and the Weinberg Theorem

TL;DR

This paper revisits the Weinberg theorem in cosmological perturbation theory, identifying conditions under which its assumptions break down in various inflationary models, thus allowing non-adiabatic modes to exist.

Contribution

The paper clarifies the assumptions behind the Weinberg theorem and highlights specific models where these assumptions are violated, leading to non-adiabatic perturbations.

Findings

Identifies loopholes in the Weinberg theorem's assumptions.

Shows violations occur in non-attractor and solid inflation models.

Provides a detailed analysis of conditions for non-adiabatic modes.

Abstract

The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.