arXiv subjects

Francisco José Maldonado Torralba

Publications and source records attributed to Francisco José Maldonado Torralba.

12 recordsLinked to original sources

arXiv2023

Averaged energy conditions for vector fields

In this work we shall obtain sufficient conditions for the appearance of singularities in gravitational theories which propagate an extra vector degree of freedom, based on the known relaxations of the singularity theorems. We study the cases of a general Proca field and a vector theory with stable self-derivative interactions. In this study we show several cases of singularities that usually would be considered as potentially singularity-free, since they violate the usual point-like energy conditions.

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arXiv2023

Junction conditions in bi-scalar Poincaré Gauge gravity

In this work, we study the junction conditions of the ghost-free subclass of quadratic Poincaré Gauge gravity, which propagates one scalar and one pseudo-scalar. For this purpose, we revisit the theory of distributions and junction conditions in gravity, giving a novel insight to the subject by introducing a convenient notation to deal with regular and singular parts. Then, we apply this formalism to bi-scalar Poincaré Gauge gravity and study some paradigmatic cases. We compare our results with the existing literature and the well-known predictions of General Relativity. We find that monopole spin densities are admissible, whereas both thin shells and double layers are allowed for the energy-momentum. Such layers can be avoided by setting appropriate continuity conditions on the dynamic fields of the theory, as well as on the Ricci scalar of the full connection and the Holst pseudo-scalar.

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arXiv2022

Vector stability in quadratic metric-affine theories

In this work we study the stability of the four vector irreducible pieces of the torsion and the nonmetricity tensors in the general quadratic metric-affine Lagrangian in 4 dimensions. The goal will be to elucidate under which conditions the spin-1 modes associated to such vectors can propagate in a safe way, together with the graviton. This highly constrains the theory reducing the parameter space of the quadratic curvature part from 16 to 5 parameters. We also study the sub-case of Weyl-Cartan gravity, proving that the stability of the vector sector is only compatible with an Einstein-Proca theory for the Weyl vector.

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arXiv2022

Instabilities in field theories: Lecture notes with a view into modified gravity

Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field redefinitions needed to reach an Einstein frame. As a consequence, they are very prone to present dynamical instabilities that could spoil any attempt to construct viable models within these frameworks. In these three lectures we introduce the most common types of instabilities that appear in field theory as well as some techniques to detect them, and supplement these contents with several examples. The goal is to understand the implications of having such pathological behaviors and the application of these notions to modified theories of gravity.

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arXiv2021

Infinite-derivative linearized gravity in convolutional form

This article aims to transform the infinite-order Lagrangian density for ghost-free infinite-derivative linearized gravity into non-local. To achieve it, we use the theory of generalized functions and the Fourier transform in the space of tempered distributions $\mathcal{S}^\prime$. We show that the non-local operator domain is not defined on the whole functional space but on a subset of it. Moreover, we prove that these functions and their derivatives are bounded in all $\mathbb{R}^3$ and, consequently, the Riemann tensor is regular and the scalar curvature invariants do not present any spacetime singularity. Finally, we explore what conditions we need to satisfy so that the solutions of the linearized equations of motion exist in $\mathcal{S}^\prime$.

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arXiv2021

Dark matter candidate from torsion

The stable pseudo-scalar degree of freedom of the quadratic Poincaré Gauge theory of gravity is shown to be a suitable dark matter candidate. We find the parameter space of the theory which can account for all the predicted cold dark matter, and constrain such parameters with astrophysical observations.

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arXiv2021

New non-singular cosmological solution of non-local gravity

We present a new bouncing cosmological solution of the non-local theory known as infinite derivative gravity, which goes beyond the recursive ansatz, ${\Box R = r_1 R +r_2}$. The non-local field equations are evaluated using the spectral decomposition with respect to the eigenfunctions of the wave operator. The energy-momentum tensor computed for this geometry turns out to be much more sensitive to the choice of the non-local form-factor, since it depends on the value of the function on a continuous infinite interval. We show that this stronger dependence on the form-factor allows us to source the geometry by the perfect fluid with the non-negative energy density satisfying the strong energy condition. We show that this bouncing behaviour is not possible in the local theories of gravity such as in general relativity or $R+R^2$ gravity sourced by a fluid which meets the non-negative energy and strong energy conditions.

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arXiv2021

New effective theories of gravitation and their phenomenological consequences

This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the structure that tells us how to perform derivatives, are studied. These theories appear when imposing that the system must be invariant under the action of the local Poincaré group. Within these theories, their stability, the conditions for the appearance of singularities, the movement of fermions, and if it is possible to find different Black Hole solutions than in Einstein's theory, is explored. Moreover, a non-local extension of the mentioned modification is proposed, which can make the theory free of instabilities and singularities at the linear limit.

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arXiv2020

Junction conditions in infinite derivative gravity

The junction conditions for the infinite derivative gravity theory ${R{+}RF(\Box)R}$ are derived under the assumption that the conditions can be imposed by avoiding the `ill-defined expressions' in the theory of distributions term by term in infinite summations. We find that the junction conditions of such non-local theories are much more restrictive than in local theories, since the conditions comprise an infinite number of equations for the Ricci scalar. These conditions can constrain the geometry far beyond the matching hypersurface. Furthermore, we derive the junction field equations which are satisfied by the energy-momentum on the hypersurface. It turns out that the theory still allows some matter content on the hypersurface (without external flux and external tension), but with a traceless energy-momentum tensor. We also discuss the proper matching condition where no matter is concentrated on the hypersurface. Finally, we explore the possible applications and consequences of our results to the braneworld scenarios and star models. Particularly, we find that the internal tension is given purely by the trace of the energy-momentum tensor of the matter confined to the brane. Consequences of the junction conditions are illustrated on two simple examples of static and collapsing stars. It is demonstrated that even without solving the field equations the geometry on one side of the hypersurface can be determined to a great extent by the geometry on the other side if the Ricci scalar is analytic. We further show that some usual star models in the general relativity are no longer solutions of the infinite derivative gravity.

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arXiv2020

Revisiting the Stability of Quadratic Poincaré Gauge Gravity

Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence of these pathological couplings results in a theory where either the axial sector or the torsion trace becomes a ghost. We conclude that imposing ghost-freedom generically leads to a non-dynamical torsion. We analyse however two special choices of parameters that allow a dynamical scalar in the torsion and obtain the corresponding effective action where the dynamics of the scalar is apparent. These special cases are shown to be equivalent to a generalised Brans-Dicke theory and a Holst Lagrangian with a dynamical Barbero-Immirzi pseudoscalar field respectively. The two sectors can co-exist giving a bi-scalar theory. Finally, we discuss how the ghost nature of the vector sector can be avoided by including additional dimension four operators.

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arXiv2019

Ghost-free higher-order theories of gravity with torsion

In this manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free.

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arXiv2019

Non-singular and ghost-free infinite derivative gravity with torsion

We present the most general quadratic curvature action with torsion including infinite covariant derivatives and study its implications around the Minkowski background via the Palatini approach. Provided the torsion is solely given by the background axial field, the metric and torsion are shown to decouple, and both of them can be made ghost and singularity free for a fermionic source.

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