Gravitational duality near de Sitter space

TL;DR

The paper establishes a one-parameter family of gravitational instantons, $\Lambda$-instantons, for any cosmological constant $\Lambda$ by introducing the $Z_{\mu\nu\rho\sigma}$ tensor and its dual, then demonstrates a linearized duality symmetry for gravity around de Sitter space using prepotentials $P_{ij}$ and $\Phi_{ij}$. It derives the quadratic Hamiltonian action in planar coordinates, resolves the scalar and vector constraints to expose the physical degrees of freedom, and defines a continuous duality rotation between the prepotentials that leaves the action invariant. The authors further obtain a manifestly dual, noncovariant form of the action by expressing it in terms of prepotentials and then in a doubled-prepotential framework, echoing the flat-space Henneaux–Teitelboim structure. The work extends known flat-space duality results to a de Sitter background, providing a promising route toward nonlinear duality properties of gravity and suggesting deeper geometric interpretations of the $Z$ tensor and Lambda-instons.

Abstract

Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic actions. The de Sitter action itself is found to be equivalent to a simple and natural quadratic action. In this paper we also describe explicitly the reparameterization and duality invariances of gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant doubling of the fields using the Hamiltonian formalism leads to first order time evolution with manifest duality symmetry. As a special case we recover the linear flat space result of Henneaux and Teitelboim by a smooth limiting process.