Generalized Gravitational S-Duality and the Cosmological Constant Problem

TL;DR

This paper explores a generalized S-duality that relates curved (A)dS spacetimes to flat Minkowski space via transformations involving the Riemann tensor and 3-form fields, offering insights into the cosmological constant problem.

Contribution

It introduces a novel S-duality framework connecting (A)dS spaces to flat spacetime and examines matter coupling to the dual metric, with implications for cosmology and gravitational theories.

Findings

Dual of (A)dS space can be flat Minkowski space under specific conditions.

Schwarzschild metric can be derived from duals of Taub-NUT-AdS metrics.

FRW cosmologies can be obtained as duals of matter-including theories.

Abstract

We study S-duality transformations that mix the Riemann tensor with the field strength of a 3-form field. The dual of an (A)dS space time - with arbitrary curvature - is seen to be flat Minkowski space time, if the 3-form field has vanishing field strength before the duality transformation. It is discussed whether matter could couple to the dual metric, related to the Riemann tensor after a duality transformation. This possibility is supported by the facts that the Schwarzschild metric can be obtained as a suitable contraction of the dual of a Taub-NUT-AdS metric, and that metrics describing FRW cosmologies can be obtained as duals of theories with matter in the form of torsion.