One-loop graviton corrections to the curvature perturbation from inflation

TL;DR

This work computes the first one-loop corrections to the curvature perturbation power spectrum arising from gravitons in single-field slow-roll inflation, using the in-in formalism and propagating results to superhorizon scales via the $\delta N$ formalism. By deriving the complete fourth-order action in the spatially flat gauge and carefully handling constraint equations, it isolates the leading tensor-scalar interaction vertices and evaluates the associated loop diagrams. The key finding is that tensor (graviton) loops contribute at the same order as scalar loops and introduce infrared logs of the form $\ln(k)$ and $\ln(k\ell)$, implying a non-negligible tensor contribution to $P_\zeta(k)$ and the necessity of a fully tensor-inclusive calculation for precision predictions. This has important implications for the self-consistency of inflationary loop corrections and the interpretation of CMB observables, since gravitons mix with scalars at nonlinear order and contribute comparably to scalar self-interactions.

Abstract

We compute one-loop corrections to the power spectrum of the curvature perturbation in single-field slow-roll inflation arising from gravitons and inflaton interactions. The quantum corrections due to gravitons to the power spectrum of the inflaton field are computed around the time of horizon crossing and their effect on the curvature perturbation is obtained on superhorizon scales through the delta-N formalism. We point out that one-loop corrections from the tensor modes are of the same magnitude as those coming from scalar self-interactions, therefore they cannot be neglected in a self-consistent calculation.

Figures (4)

• Figure 1: Diagrammatic representation of the one loop corrections to the power spectrum of $\delta\phi$ from scalar modes to leading ($\sim {\epsilon}^{0}$) order in slow-roll.
• Figure 2: Next-to-leading ($\sim \sqrt{\epsilon}$) order one loop corrections from scalar modes to the power spectrum of $\delta\phi$.
• Figure 3: Diagrammatic representation of the (tensor mode) corrections from $H_{I}^{(4)}$ to the power spectrum of $\delta\phi$.
• Figure 4: Diagrammatic representation of the (tensor mode) corrections from $H_{I}^{(3)}$ to the power spectrum of $\delta\phi$. Notice that this diagram is not slow-roll suppressed compared to the one in Fig.$3$ whereas this is not the case for scalar modes (see Fig.$1$ and Fig.$2$).