Gravity from Spinors

TL;DR

This paper explores a unified spinor-based approach to gravity, suggesting modifications to Einstein's equations due to global Lorentz symmetry, consistent with current tests but implying local Lorentz symmetry is only partially tested.

Contribution

It introduces a systematic derivative expansion of spinor gravity, revealing new invariants in the gravitational action and analyzing their observational implications.

Findings

One-loop approximation yields a consistent effective gravitational theory.

Global Lorentz symmetry modifications are compatible with current cosmological tests.

Local Lorentz symmetry remains only partially constrained by observations.

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.