MacDowell-Mansouri $\sigma$-model

Abstract

Standard pre-geometric mechanisms reproduce the ΛCDM model but lack a natural source for inflation. We propose a mechanism for the emergence of scalar-coupled topological terms by extending the Lie algebra of a MacDowell-Mansouri model to a Lie algebroid. These terms are commonly regarded as a source for cosmological inflation in effective string actions. The theory reduces to the scalar-tensor theory belonging to the Horndeski class, and reproduces inflationary dynamics that meet existing constraints (Planck/BICEP/Keck and GW170817).