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Effective topological field theories describe the properties of Diracfermions in the low-energy regime. In this work, we introduce a new emergentgravity model by considering Dirac fermions invariant under local de Sittertransformations in four-dimensional open manifolds. In the context of Cartangeometry, fermions couple to spacetime through a $Spin(5)$ Cartan connectionthat can be decomposed in spin connection and tetrads. In presence of agravitational instanton background, we show that the corresponding effectivetopological field theory becomes a dynamical gravitational theory with apositive cosmological constant and Barbero-Immirzi parameter. At classicallevel and in absence of matter, this theory is compatible with generalrelativity.

Gravitational behavior of an effective topological field theory in a gravitational instanton background