arXiv subjects

Bastian Grez

Publications and source records attributed to Bastian Grez.

5 recordsLinked to original sources

arXiv2025

Decomposition of the connection in affine models of gravity: Can the connection tell us something about the metric?

In physics geometrical connections are the mean to create models with local symmetries (gauge connections), as well as general diffeomorphisms invariance (affine connections). Here we study the irreducible tensor decomposition of connections on the tangent bundle of an affine manifold as used in the polynomial affine model of gravity. This connection is the most general linear connection, which allows us to build metric independent, diffeomorphism invariant models. This set up includes parts of the connection that are associated with conformal and projective transformations.

gr-qc↗

arXiv2024

A polynomial affine model of gravity: after ten years

The polynomial affine model of gravity was proposed as an alternative to metric and metric-affine gravitational models. What at the beginning was thought as a source of unpredictability, the presence of many terms in the action, turned out to be a milestone, since it contains all possible combinations of the fields compatible with the covariance under diffeomorphisms. Here, we present a review of the advances in the analysis of the model after ten years of its proposal, and sketch the guideline of our future perspectives.

gr-qc↗

arXiv2024

Cosmological Solutions in Polynomial Affine Gravity with Torsion

The Polynomial Affine Gravity is an alternative gravitational model, where the interactions are mediated solely by the affine connection, instead of the metric tensor. In this paper, we explore the space of solutions to the field equations when the torsion fields are turned on, in a homogeneous and isotropic (cosmological) scenario. We explore various metric structures that emerge in the space of solutions.

gr-qc↗

arXiv2023

Inflationary scenarios in an effective polynomial affine model of gravity

In this paper we inquire inflationary scenarios built on a simplified version of the polynomial affine model of gravity. Given the absence of a metric tensor in the formulation of the model, we build a \emph{kinetic term} contracting the derivatives of scalar field with the most general $(2,0)$-tensor density build using the affine connection, and introduce a self-interacting potential via a scaling of the volume form. We analyse the cosmological solutions derived from this setup.

gr-qc↗

arXiv2022

Polynomial affine model of gravity in three-dimensions

In this work, we explore a three-dimensional formulation of the polynomial affine model of gravity, which is a model that extends general relativity by relaxing the equivalence principle through the exclusion of the metric from the set of fundamental fields. In particular, in an attempt to gain insight of the role of the torsion and nonmetricity in the gravitational models, we consider homogeneous and isotropic cosmological models, for which their solutions are classified in a \emph{decisions tree}. We also show a few of these explicit solutions that allow the definition of (alternative/emergent) metrics derived from the connection.

gr-qc↗