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

Abstract

In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation $\mathcal{R}$ to non-attractor inflationary regimes. We show that both modes of $\mathcal{R}$ 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 $\mathcal{R}$, not even in the $k\to 0$ 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. We have then shown that the perturbative $\delta N$ definition in terms of difference between the number of e-foldings of different gauges, can be extended non-perturbatively at leading order in gradient expansion. Nevertheless, the computer friendly definition in terms of the difference of e-foldings obtained from the evolution of a local FRW Universe, respectively with perturbed and un-perturbed initial conditions, might only give information about the linear order curvature perturbations, contrary to what stated in the literature.

18 pages. Explanations and minor corrections added. Results unchanged. Accepted for publication in JCAP

References in corpus (3)

• Primordial Black Holes and Slow-Roll Violation
• Review on stochastic approach to inflation
• Stochastic inflation at all order in slow-roll parameters: foundations

Cited by in corpus (6)

• Hamiltonian formalism for cosmological perturbations: fixing the gauge
• On the Hamilton-Jacobi approach to inflation beyond slow roll
• The validity of separate-universe approach in transient ultra-slow-roll inflation
• $\delta N$ formalism with gradient interactions
• Effect of stochastic kicks on primordial black hole abundance and mass via the compaction function
• Separate universe in multifield inflation: a phase-space approach