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Abstract. We review many quantum aspects of torsion theory and discuss the possibility of the space-time torsion to exist and to be detected. The paper starts, in Chapter 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Chapter 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Chapter 4 is devoted to the action of spinning and spinless particles in a space-time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Chapter 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion-torsion interaction implies that torsion itself has a huge mass, and can not be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Chapter 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.

In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the "cosmological constant" is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time. At higher energies the calculation is performed in a sharp cut off approximation. We assess, in two different frameworks, whether the scaling dependences of the cosmological and gravitational constants spoil primordial nucleosynthesis. Finally, the cosmological implications of the running of the cosmological constant are discussed.

A large value of the cosmological constant (CC) is induced in the Standard Model (SM) of Elementary Particle Physics because of Spontaneous Symmetry Breaking. To provide a small value of the observable CC one has to introduce the vacuum term which cancels the induced one at some point in the very far infrared cosmic scale. Starting from this point we investigate whether the cancellation is preserved at different energy scales. We find that the running of the Higgs mass, couplings and the vacuum term inevitably result in a scaling dependence of the observable value. As a consequence one meets a nonzero CC at an energy scale comparable to the typical electron neutrino mass suggested by some experiments, and the order of magnitude of this constant is roughly the one derived from recent supernovae observations. However the sign of it is negative -opposite to what is suggested by these observations. This discrepancy may be a hint of the existence of an extra very light scalar, perhaps a Cosmon-like dilaton, which should essentially decouple from the SM Lagrangian, but that it nevertheless could mediate new macroscopic forces in the submillimeter range.