Vacuum quantum fluctuations in curved space and the theory of gravitation

The presence of the action (1) leads to a “metrical elasticity” of space, i.e., to generalized forces which oppose the curving of space. Here we consider the hypothesis which identifies the action (1) with the change in the action of quantum fluctuations of the vacuum if space is curved. Thus, we consider the metrical elasticity of space as a sort of level displacement effect (cf. also [1a]). In present-day quantum field theory it is assumed that the energy momentum tensor of the quantum fluctuations of the vacuum T k(0) and the corresponding action S(0), formally proportional to a divergent integral