Cosmological Correlators in Gauge Theory and Gravity from EAdS

TL;DR

This work broadens the dS–$EAdS$ map beyond scalars to gauge bosons and gravitons by refining the Schwinger–Keldysh to $EAdS$ reformulation in Mellin space. It provides explicit Mellin-space expressions for bulk-to-bulk and bulk-to-boundary propagators of spinning fields in $EA$dS, and shows how late-time dS correlators decompose into sums of $EAdS$ Witten diagrams with precise sine-phase factors and $ ext{Δ}_"+, ext{Δ}_-$ boundary data. The paper delivers concrete perturbative recipes for scalar QED, pure YM, and Einstein gravity, including contact and exchange diagrams, and treats subtleties arising in even boundary dimensions and the $ u ightarrow -i n$ exceptional cases via an $EAdS$ harmonic function. The results offer a streamlined, nonperturbative-friendly framework to study cosmological correlators with spinning fields, enabling the import of AdS/CFT and conformal bootstrap techniques into the inflationary setting. Overall, the work equips researchers with actionable Mellin-space propagator formulas and diagrammatic rules to compute late-time cosmological correlators in gauge theory and gravity.

Abstract

In this work we examine in more detail the map between late-time correlators in de Sitter space and boundary correlators in Euclidean anti-de Sitter space, elaborating on the general construction presented in arXiv:2007.09993 and arXiv:2109.02725 for EFTs of bosonic spinning fields. This map may be phrased as an equivalence between the generating functional of late-time correlators in the Schwinger-Keldysh formalism and the generating functional for boundary correlators in the corresponding EAdS theory. We extend the construction to gauge bosons and gravitons, and clarify additional subtleties that appear in even boundary dimensions. Finally, we emphasise that the relation between dS and EAdS propagators is manifest in Mellin space, and we provide new expressions for gauge-boson and graviton propagators. These results provide a streamlined framework for the study of cosmological correlators involving spinning fields.

Figures (6)

• Figure 1: This figure illustrates the Schwinger-Keldysh counter (blue line) and the rotation of each branch to EAdS (yellow line) under the Wick rotations \ref{['wickzeta']}.
• Figure 2: Graphical summary of the rules \ref{['bubuwick']}, \ref{['bubowick']}, \ref{['measurewick']} and \ref{['vertexwick']}, derived in Sleight:2020obcSleight:2021plv, recasting perturbation theory for late-time correlators in the Schwinger-Keldysh formalism in terms of Witten diagrams in EAdS. The dS late time boundary is the horizontal grey line and the EAdS boundary the grey circle.
• Figure 3: Plot of the $u$ poles from the factors $\Gamma\left(u\pm \frac{i\nu}{2}\right)$ in the Mellin space representation \ref{['EAdS scalar prop Mellin bubu']} of the bulk-to-bulk propagator. The poles from $\Gamma\left(u - \frac{i\nu}{2}\right)$, which generate the falloff $z^{\frac{d}{2}-i\nu+2n}$ as $z \to 0$, are denoted by solid blue circles and the poles from $\Gamma\left(u + \frac{i\nu}{2}\right)$, generating the falloff $z^{\frac{d}{2}+i\nu+2n}$, are the hollow blue circles. The zeros from the factor $\omega_{\nu}(u,\bar{u})$ are the green crosses, which cancel the poles from $\Gamma\left(u - \frac{i\nu}{2}\right)$. Likewise, the zeros of $\omega_{-\nu}(u,\bar{u})$ would cancel the poles from $\Gamma\left(u + \frac{i\nu}{2}\right)$. To plot the poles we assumed that $\nu \in \mathbb{R}$, which corresponds to unitary Principal Series representations of the dS isometry group.
• Figure 4: For $\nu = -in$ the two families of poles in the Mellin variable $u$, illustrated in figure \ref{['fig::upoles']}, both collapse along the real axis and coincide for all but a finite number of poles. This gives an infinite number of double poles and a finite number of single poles.
• Figure 5: The three-point contact diagram in dS scalar QED is proportional to the corresponding three-point contact Witten diagram in EAdS. The proportionality constant is given in \ref{['3pt qed ds to ads']}.