A Vacuum Solution with Torsion in Higher-Derivative Gravity

TL;DR

This paper presents a vacuum solution with torsion in higher-derivative gravity, revealing that vacuum can possess large torsion and that the Einstein-Hilbert action emerges from quadratic curvature expansion around a nonzero vacuum field.

Contribution

It introduces a novel vacuum solution with torsion in quadratic Riemann-curvature gravity and links it to the derivation of Einstein-Hilbert action from quadratic curvature.

Findings

Vacuum can have a nonzero torsion field.

The Einstein-Hilbert action can be derived from quadratic curvature expansion.

The cosmological constant is zero in this vacuum solution.

Abstract

In this paper, we provide a vacuum solution with torsion in quadratic Riemann-curvature gravity. Physically, the solution means that vacuum can have a nonzero vacuum field with large torsion. We show that the Einstein-Hilbert action can be derived if we expand the quadratic curvature of the Lagrangian in a torsion-free Riemannian space-time around a nonzero vacuum field. We also show that the cosmological constant caused by a nonzero vacuum field is equal to zero.