arXiv subjects

Oscar Castillo-Felisola

Publications and source records attributed to Oscar Castillo-Felisola.

At least 19 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↗

arXiv2025

On the Kaluza-Klein geometric theory in affine spaces

In this work, we develop a generalization of Kaluza-Klein theory by considering a purely affine framework, without assuming a prior metric structure. We formulate the dimensional reduction using the geometry of principal fiber bundles and the Ehresmann connection, introducing adapted bases that allow an explicit decomposition of tensors, vectors, and connections. This formalism provides a natural geometric definition of the electromagnetic field as the difference between the horizontal space and the space generated by the observer's frame. We demonstrate that the presence of a nontrivial electromagnetic field requires the non-integrability of the horizontal distribution, and we derive a complete ansatz for decomposing the affine connection into fields defined on the reduced space. Under assumptions such as vanishing torsion, autoparallel fibers, and suitable normalization conditions, we show that the reduced theory corresponds to the Einstein-Maxwell system for purely radiative electromagnetic fields. Furthermore, we propose an interpretation where the metric emerges dynamically from the affine structure through the dynamics of the electromagnetic field.

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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.

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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.

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arXiv2024

A model for cosmological perturbations in affine gravity

In this paper, we present the cosmological perturbation formalism for theories within the framework of affine gravity. These theories are distinguished by their connection, devoid of any metric. Our approach involves segregating perturbations into symmetric and antisymmetric components (related to torsion), each further decomposed into irreducible elements, namely scalars, pseudoscalars, vectors, pseudovectors, 2-tensors, and 3-tensors. Finally, we have fully addressed the gauge freedom in this context.

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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.

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arXiv2023

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.

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arXiv2022

Polynomial affine gravity in 3+1 dimensions

The polynomial affine gravity is an alternative model of gravity whose fundamental field is the affine connection, and it is invariant under the complete group of diffeomorphisms. In 3+1 dimensions the field equations generalise those of Einstein--Hilbert, the coupling constants are dimensionless, the action has a finite numbers of term, and although the action does not involve a (fundamental) metric, some metric tensor fields might \emph{emerge} from the connection. Provided a cosmological ansatz, the properties of diverse cosmological models are discussed.

gr-qc↗

arXiv2022

Cadabra and Python algorithms in General Relativity and Cosmology I: Generalities

The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface. The current paper focuses on fairly generic applications in gravitational theories, including the use of differential forms, the derivation of field equations and the construction of their solutions. A follow-up paper discusses more specific applications related to the analysis of gravitational waves.

gr-qc↗

arXiv2022

Cadabra and Python algorithms in General Relativity and Cosmology II: Gravitational Waves

Computer Algebra Systems (CASs) like Cadabra Software play a prominent role in a wide range of research activities in physics and related fields. We show how Cadabra language is easily implemented in the well established Python programming framework, gaining excellent flexibility and customization to address the issue of tensor perturbations in General Relativity. We obtain a performing algorithm to decompose tensorial quantities up to any perturbative order of the metric. The features of our code are tested by discussing some concrete computational issues in research activities related to first/higher-order gravitational waves.

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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.

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arXiv2021

Aspects of the polynomial affine model of gravity in three dimensions

The polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.

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arXiv2019

Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine Gravity

Starting from an affinely connected space, we consider a model of gravity whose fundamental field is the connection. We build up the action using as sole premise the invariance under diffeomorphisms, and study the consequences of a cosmological ansatz for the affine connection in the torsion-free sector. Although the model is built without requiring a metric, we show that the nondegenerated Ricci curvature of the affine connection can be interpreted as an \emph{emergent} metric on the manifold. We show that there exists a parametrization in which the $(r,φ)$-restriction of the geodesics coincides with that of the Friedman--Robertson--Walker model. Additionally, for connections with nondegenerated Ricci we are able to distinguish between space-, time- and null-like self-parallel curves, providing a way to differentiate \emph{trajectories} of massive and massless particles.

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arXiv2019

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 yield the cosmological field equations of General Relativity coupled with a perfect fluid, pointing toward a geometrical emulation of---what is interpreted in General Relativity as---matter effects.

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arXiv2019

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.

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arXiv2019

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.

hep-ph↗

arXiv2018

Dirac spinors and their application to Bianchi-I space-times in 5 dimensions

We consider a five-dimensional Einstein--Cartan 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 unlike what happens in the four-dimensional instance: 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.

gr-qc↗

arXiv2017

Corrections to (pseudo)scalars decay into a fermion pair from gravitational torsion

We study the contribution of the torsion-descendent four-fermion contact interaction to the decay width of a neutral (pseudo)scalar field into a fermion pair. This new interaction comes from the existence of gravitational torsion in models with extra dimensions. Additionally, we exemplify the formalism with two examples: first, the variation of the considered branching ratio of the Higgs in the context of the standard model, and second the proper variations of the scalar and pseudo scalar fields of the type II-1 two Higgs doublets model.

hep-ph↗