A Vacuum Solution with Torsion in Higher-Derivative Gravity

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.