TL;DR
This paper reviews a class of metric-independent, generally covariant theories in four dimensions that extend general relativity, discussing their modifications, renormalizability, matter coupling, and physical properties.
Contribution
It provides a comprehensive status report on non-metric gravity theories, highlighting their formulation, properties, and potential as modified gravity models.
Findings
These theories propagate two degrees of freedom.
They include general relativity in Plebanski formulation.
Current understanding of their renormalizability and matter coupling.
Abstract
We review the status of a certain (infinite) class of four-dimensional generally covariant theories propagating two degrees of freedom that are formulated without any direct mention of the metric. General relativity itself (in its Plebanski formulation) belongs to the class, so these theories are examples of modified gravity. We summarize the current understanding of the nature of the modification, of the renormalizability properties of these theories, of their coupling to matter fields, and describe some of their physical properties.
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