Vacuum tunneling in gravity

Topologically non-trivial vacuum structure in gravity models with Cartan variables (vielbein and contortion) is considered. We study the possibility of vacuum space-time tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology the tunneling between non-trivial topological vacuums can be realized by means of Eguchi-Hanson gravitational instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum tunneling can be provided by means of contortion quantum fluctuations. We define double self-duality condition for the contortion and give explicit self-dual configurations which can contribute to vacuum tunneling amplitude.