All plus four point (A)dS graviton function using generalized on-shell recursion relation

TL;DR

This paper introduces a generalized on-shell recursion relation to compute four-graviton amplitudes in (A)dS space, simplifying calculations and aiding cosmological studies without relying on traditional Feynman-Witten diagrams.

Contribution

It develops a novel recursion method for AdS graviton amplitudes using complexified external momenta, applicable in three dimensions, enhancing computational efficiency in cosmological contexts.

Findings

Derived explicit four-graviton amplitude expressions in AdS space.

Demonstrated the method's effectiveness through symbolic and numerical results.

Discussed the approach's advantages and limitations for future research.

Abstract

This paper presents a calculation of the four gravitons amplitude in (Anti)-de Sitter space, focusing specifically on external gravitons with positive helicity. To achieve this, we employ a generalized recursion method that involves complexifying all external momentum of the graviton function, which results in the factorization of AdS graviton amplitudes and eliminates the need for Feynman-Witten diagrams. Our calculations were conducted in three boundary dimensions, with a particular emphasis on exploring cosmology and aiding the cosmological bootstrap program. To compute the expression, we utilized the three-dimensional spinor helicity formalism. The final expression was obtained by summing over residues of physical poles, and we present both symbolic and numerical results. Additionally, we discuss the advantages and limitations of this approach, and highlight potential opportunities for future research.