Invariance under complex transformations, and its relevance to the cosmological constant problem

TL;DR

This paper introduces a novel symmetry argument based on complex transformations relating de Sitter and Anti-de Sitter spaces, suggesting a vacuum state with zero vacuum energy, offering a new perspective on the cosmological constant problem.

Contribution

It proposes a new symmetry approach involving complex transformations that could lead to a vacuum state with zero energy, expanding theoretical understanding of vacuum energy.

Findings

Symmetry relates de Sitter and Anti-de Sitter spaces via analytic continuation.

Dropping boundary and hermiticity conditions yields equal positive and negative energy states.

The approach suggests a new direction for addressing the cosmological constant problem.

Abstract

In this paper we study a new symmetry argument that results in a vacuum state with strictly vanishing vacuum energy. This argument exploits the well-known feature that de Sitter and Anti- de Sitter space are related by analytic continuation. When we drop boundary and hermiticity conditions on quantum fields, we get as many negative as positive energy states, which are related by transformations to complex space. The paper does not directly solve the cosmological constant problem, but explores a new direction that appears worthwhile.