Multidimensional Classical and Quantum Wormholes in Models with Cosmological Constant

TL;DR

This paper explores classical and quantum wormhole solutions in a multidimensional cosmological model with a negative cosmological constant, Ricci-flat spaces, and a scalar field, revealing conditions for wormhole existence.

Contribution

It presents new classical and quantum wormhole solutions in multidimensional models with a cosmological constant and scalar fields, including cases with spontaneous compactification.

Findings

Classical and quantum wormholes exist for negative cosmological constant and Ricci-flat spaces.

Wormhole solutions are found for models with a single Ricci-flat internal space.

Conditions for spontaneous compactification with wormhole solutions are identified.

Abstract

A multidimensional cosmological model with space-time consisting of $n (n \ge 2)$ Einstein spaces $M_{i}$ is investigated in the presence of a cosmological constant $\Lambda$ and a homogeneous minimally coupled scalar field $\varphi(t)$ as a matter source. Classical and quantum wormhole solutions are obtained for $\Lambda < 0$ and all $M_{i}$ being Ricci-flat. Classical wormhole solutions are also found for $\Lambda < 0$ and only one of the $M_{i}$ being Ricci-flat for the case of spontaneous compactification of the internal dimensions with fine tuning of parameters.