Cosmological Dressing Rules

Abstract

The basic observables in cosmology are known as in-in correlators. Recent calculations have revealed that in-in correlators in four dimensional de Sitter space exhibit hidden simplicity stemming from a close relation to scattering amplitudes in flat space. In this paper we explain how to make this property manifest by dressing flat space Feynman diagrams with certain auxiliary propagators. These dressing rules are derived for conformally coupled and massless scalar theories and we show that they reproduce the same infrared divergences predicted by the Schwinger-Keldysh formalism.

Figures (15)

• Figure 1: Diagrammatic representation of propagators which feature in the shadow formalism, the formulae for which are given in \ref{['eq:EAdSProps']}. $\phi_+$ fields have $\nu>0$ and $\phi_-$ fields have $\nu<0$. Only the latter appear as external legs.
• Figure 2: Three-point contact diagram in conformally coupled $\phi^3$ from the shadow formalism and the dressing rules.
• Figure 3: Shadow diagrams contributing to the four-point correlator at tree level in conformally coupled $\phi^3$. Here $\vec{y}_{12}=\vec{k}_1+\vec{k}_2.$
• Figure 4: The two dressed diagrams which contribute to the four-point conformally coupled correlator at tree level. Recall that dotted auxiliary propagators only occur in pairs, so there are no diagrams with both types.
• Figure 5: Shadow diagrams with a single suppressed vertex in conformally coupled $\phi^3$.