Gravitation and Cosmology in Generalized (1+1)-dimensional dilaton gravity

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The actions of the ``R=T'' and string-inspired theories of gravity in (1+1) dimensions are generalized into one single action which is characterized by two functions. We discuss differing interpretations of the matter stress-energy tensor, and show how two such different interpretations can yield two different sets of field equations from this action. The weak-field approximation, post-Newtonian expansion, hydrostatic equilibrium state of star and two-dimensional cosmology are studied separately by using the two sets of field equations. Some properties in the ``R=T'' and string-inspired theories are shown to be generic in the theory induced by the generalized action.