Gravity from Spinors

Abstract

We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of Einstein's equations due to the lack of local Lorentz-symmetry. We explore the generalized gravity with global instead of local Lorentz symmetry in first order of a systematic derivative expansion. At this level diffeomorphisms and global Lorentz symmetry allow for two new invariants in the gravitational effective action. The one which arises in the one loop approximation to spinor gravity is consistent with all present tests of general relativity and cosmology. This shows that local Lorentz symmetry is tested only very partially by present observations. In contrast, the second possible new coupling is severely restricted by present solar system observations.