Progress toward a theory of supergravity

As a new approach to supergravity, an action containing only vierbein and Rarita-Schwinger fields ($V_{a\mu }$ and ${\psi }_{\mu }$) is presented together with supersymmetry transformations for these fields. The action is explicitly shown to be invariant except for a ${\psi }^5$ term in its variation. This term may also vanish, depending on a complicated calculation. (Added note: This term has now been shown to vanish by a computer calculation, so that the action presented here does possess full local supersymmetry.)