Gravitational duality near de Sitter space

TL;DR

This paper explores gravitational duality in de Sitter space, defining Lambda-instantons, establishing bounds on the de Sitter action, and revealing duality invariances in linearized gravity through Hamiltonian formalism.

Contribution

It introduces Lambda-instantons for any cosmological constant and demonstrates duality invariances in linearized gravity around de Sitter space.

Findings

Euler characteristic bounds the de Sitter action

De Sitter action is equivalent to a quadratic action

Duality invariance is manifest in Hamiltonian formalism

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.