Conservation of the nonlinear curvature perturbation in generic single-field inflation

TL;DR

This paper demonstrates that the nonlinear curvature perturbation remains conserved on superhorizon scales in single-field inflation models with an attractor regime, extending known results to a broad class of scalar field theories.

Contribution

It generalizes the conservation of nonlinear curvature perturbation to a wide range of scalar field theories, including those with complex kinetic terms, under attractor conditions.

Findings

Conservation holds for scalar fields in attractor regimes.

Galileon theories require gravitational equations to confirm conservation.

The result applies to a broad class of single-field inflation models.

Abstract

It is known that the curvature perturbation on uniform energy density (or comoving or uniform Hubble) slices on superhorizon scales is conserved to full nonlinear order if the pressure is only a function of the energy density (ie, if the perturbation is purely adiabatic), independent of the gravitational theory. Here we explicitly show that the same conservation holds for a universe dominated by a single scalar field provided that the field is in an attractor regime, for a very general class of scalar field theories. However, we also show that if the scalar field equation contains a second time derivative of the metric, as in the case of the Galileon theory, one has to invoke the gravitational field equations to show the conservation.