Beyond Einstein: A Polynomial Affine Model of Gravity

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds—with or without cosmological constant—as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang-Mills theory known as the Stephenson-Kilmister-Yang (SKY) theory. Additionally, we find a generalisation of a minimally coupled massless scalar field in general relativity within a “minimally” coupled scalar field in this affine model. Finally, we present the road map to finding general solutions to the effective field equations with either isotropic or cosmologic (i.e., homogeneous and isotropic) symmetry

Does the metric play a fundamental role in the building of gravitational models?

The idea that General Relativity could be an effective model, of a yet unknown theory of gravity, has gained momentum among theoretical physicists. The polynomial affine model of gravity is an alternative model of affine gravity that possesses many desirable features to pursue a quantum theory of gravitation. In this paper we argue that such features are a consequence of the lack of a metric structure in the building of the model, even though a emergent metric could be defined. The model introduces additional degrees of freedom associated to the geometric properties of the space, which might shed light to understand the nature of the dark sector of the Universe. When the model is coupled to a scalar field, it is possible to define inflationary scenarios

Cosmological Solutions to Polynomial Affine Gravity in the Torsion-Free Sector

We find possible cosmological models of the polynomial affine gravity described by connections that are either compatible or not with a metric. When possible, we compare them with those of general relativity. We show that the set of cosmological vacuum solutions in general relativity are a subset of the solutions of polynomial affine gravity. In our model, the cosmological constant appears as an integration constant, and, additionally, we show that some forms of matter can be emulated by the affine structure—even in the metric compatible case. In the case of connections not compatible with a metric, we obtain formal families of solutions, which should be constrained by physical arguments. We show that for a certain parametrisation of the connection, the affine Ricci-flat condition yields the cosmological field equations of general relativity coupled with a perfect fluid, pointing towards a geometrical emulation of—what is interpreted in general relativity as—matter effects

Dirac Spinors and Their Application to Bianchi-I Space-Times in 5 Dimensions

We consider a five-dimensional Einstein\u2013Sciama\u2013Kibble spacetime upon which Dirac spinor fields can be defined. Dirac spinor fields in five and four dimensions share many features, like the fact that both are described by four-component spinor fields, but they are also characterized by strong differences, like the fact that in five dimensions we do not have the possibility to project on left-handed and right-handed chiral parts: we conduct a polar decomposition of the spinorial fields, so to highlight all similarities and discrepancies. As an application of spinor fields in five dimensions, we study Bianchi-I spacetimes, verifying whether the Dirac fields in five dimensions can give rise to inflation or dark-energy dominated cosmological eras or not