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

High-dimensional neutrino masses

For Majorana neutrino masses the lowest dimensional operator possible is the Weinberg operator at $d=5$. Here we discuss the possibility that neutrino masses originate from higher dimensional operators. Specifically, we consider all tree-level decompositions of the $d=9$, $d=11$ and $d=13$ neutrino mass operators. With renormalizable interactions only, we find 18 topologies and 66 diagrams for $d=9$, and 92 topologies plus 504 diagrams at the $d=11$ level. At $d=13$ there are already 576 topologies and 4199 diagrams. However, among all these there are only very few genuine neutrino mass models: At $d=(9,11,13)$ we find only (2,2,2) genuine diagrams and a total of (2,2,6) models. Here, a model is considered genuine at level $d$ if it automatically forbids lower order neutrino masses {\em without} the use of additional symmetries. We also briefly discuss how neutrino masses and angles can be easily fitted in these high-dimensional models.Comment: Coincides with published version in JHE

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