CPTM Discrete Symmetry, Quantum Wormholes and Cosmological Constant Problem

Abstract

We discuss the consequences of the charge, parity, time, and mass (CPTM) extended reversal symmetry for the problems of the vacuum energy density and value of the cosmological constant. The results obtained are based on the framework with the separation of extended space-time of the interest on the different regions connected by this symmetry with the action of the theory valid for the full space-time and symmetrical with respect to the extended CPTM transformations. The cosmological constant is arising in the model due the gravitational interactions between the different parts of the space-time trough the quantum non-local vertices. It is proposed that the constant’s value depends on the form and geometry of the vertices that glue the separated parts of the extended solution of Einstein equations determining, in turn, its classical geometry. The similarity of the proposed model to the bimetric theories of gravitation is also discussed.