We describe gauge theories that allow one to retrieve a large class of gravitational theories, including MacDowell-Mansouri gravity and its topological extension to loop quantum gravity via the Pontryagin characteristic class involving the Nieh-Yan term. Considering symmetric spaces parametrized by mutations allows one to naturally obtain a bare cosmological constant that in particular cases gives rise to a positive effective cosmological constant while having an anti–de Sitter (AdS) spacetime. Two examples are studied, Lorentzian geometry (including dS and AdS spacetimes) and Lorentz $\times$ Weyl geometry. In the latter case, we prove that adding a term dependent on torsion and dilations makes the equations of motion exhibit a secondary source for curvature in addition to the usual energy-momentum tensor. This additional source is expressed in terms of the spin density of matter, torsion, and their variations. Finally, we show that the $\mathrm{gauge}+\mathrm{matter}$ actions constructed from invariant polynomials are asymptotically topological if one assumes a vanishing bare cosmological constant together with gauge and matter fields having compact support.

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• Alternative gravity theories
• Cosmological constant
• Quantum gravity