Notes on recentU 4 theories of gravitation

Some of the proposed Lagrangians and their corresponding field equations for a gravitational theory based on a Riemann-Cartan space with metric-compatible connection (U ₄, theory) are compared and a new one is suggested. This Lagiangian, and that of P. von der Heyde and F. W. Hehl et al. are examined applying the Gordon-decomposition argument. Finally, Einstein's field equations with cosmological term are shown to be included in some sense, but the cosmological constant naturally has microphysical origin. To simplify notation, Cartan's calculus is used throughout.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung in österreich, project No. 3666.Most of this work was carried out during the stay at the 6th Course of the International School of Cosmology and Gravitation at Erice, 1979.