An update on adiabatic modes in cosmology and $\delta$N formalism

Understand

In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation $\cal R$ to non-attractor inflationary regimes.

• We show that both modes of $\cal R$ are related to a symmetry of the perturbative equations in the Newtonian gauge.
• As a byproduct, we clarify that adiabaticity does not generally imply constancy of $\cal R$, not even in the $k\rightarrow 0$ limit.
• We then show that there exist non-equivalent definitions of $\delta N$ that would reproduce $\mathcal{R}$ or the uniform density curvature perturbation $\zeta$ at linear order.