Curvature Perturbations in the Effective Field Theory of Inflation

Abstract

We discuss the difference between various gauge-invariant quantities typically used in single-field inflation, namely synchronous ${\zeta }_s$, comoving ${\zeta }_c$, and unitary ${\zeta }_u$ curvatures. We show that conservation of ${\zeta }_c$ outside the horizon is quite restrictive on models as it leads to conservation of ${\zeta }_s$ and ${\zeta }_u$, whereas the reverse does not hold. We illustrate the consequence of these differences with two inflationary models: ultra-slow-roll (USR) and braiding-ultra-slow-roll (BUSR). In USR, we show that out of the three curvatures, only ${\zeta }_s$ is conserved outside the horizon, and we connect this result to the concepts of separate universe and the usage of the $\delta N$ formalism. We find that even though ${\zeta }_s$ is conserved, there is still a mild violation of the separate universe approximation in the continuity equation. Nevertheless, the $\delta N$ formalism can still be applied to calculate the primordial power spectrum of some gauge-invariant quantities such as ${\zeta }_u$, although it breaks down for others such as the uniform-density curvature. In BUSR, we show that both ${\zeta }_u$ and ${\zeta }_s$ are conserved outside the horizon, but take different values. Additionally, since ${\zeta }_u\ne {\zeta }_c$ we find that the prediction for observable curvature fluctuations after inflation does not reflect ${\zeta }_c$ at horizon crossing during inflation and moreover involves not just ${\zeta }_u$ at that epoch but also the manner in which the braiding phase ends.

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Cited by in corpus (3)

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• Effective field theory of degenerate higher-order inflation
• Unifying attractor and non-attractor models of inflation under a single soft theorem