Sebastián Bahamonde

Teleparallel gravity (TG) has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we give a comprehensive introduction to how teleparallel geometry is developed as a gauge theory of translations together with all the other properties of gauge field theory. This relates the geometry to the broader metric-affine approach to forming gravitational theories where we describe a systematic way of constructing consistent tele

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is th

We consider the cosmology derived from <i>f</i>(<i>T</i>, <i>B</i>) gravity where <i>T</i> is the torsion scalar and [Formula: see text] a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel <i>f</i>(<i>T</i>) gravity, the curvature <i>f</i>(<i>R</i>) gravity, and the teleparallel-curvature <i>f</i>(<i>R</i>, <i>T</i>) gravity, which are particular cases of <i>f</i>(<i>T</i>, <i>B</i>). We adopt the Noether Symmetry Approach to study t

Horndeski gravity is the most general scalar tensor theory, with a single scalar field, leading to second-order field equations and after the GW170817 it has been severely constrained. Since this theory is very important in modified gravity, it is then worth studying possible similar theories starting from other frameworks. In this paper, we study the analog of Horndeski's theory in the teleparallel gravity framework where gravity is mediated through torsion instead of curvature. We show that, e

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion f(Tax,Tten,Tvec), where Tax,Tten and Tvec are squares of the axial, tensor and vector components of torsion, respectively. This is the most general (well-motivated) second order teleparallel theory of gravity that can be constructed from the torsion tensor. Different particular second order theories can be recovered from this theor

A gravitational theory of a scalar field nonminimally coupled with torsion and a boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of the Noether gauge symmetry approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficien

Motivated by recent proposals of possible wormhole existence in galactic halos, we analyze the cosmological evolution of wormhole solutions in modified $f(R)$ gravity. We construct a dynamical wormhole that asymptotically approaches a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universe, with supporting material going to the perfect isotropic fluid described by the equation of state for a radiation- and matter-dominated universe respectively. Our analysis is based on an approximation of a sm

In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model $f(R,{\mathbf{T}}^{\mathbf{2}})$, where $R$ represents the scalar curvature and ${\mathbf{T}}^{\mathbf{2}}$ the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions $f(R,{\mathbf{T}}^{\mathbf{2}})$, we have studied the structure of the phase space and the physical implications of the energ

In this paper we study the occurrence of accelerating universe versus decelerating universe between the F(R) gravity frame (Jordan frame) and non-minimally coupled scalar field theory frame, and the minimally coupled scalar field theory frame (Einstein frame) for various models. As we show, if acceleration is imposed in one frame, it will not necessarily correspond to an accelerating metric when transformed in another frame. As we will demonstrate, this issue is model and frame-dependent but it

Among modified theories of gravity, the teleparallel $f(T)$ gravity is an intensively discussed model in the literature. The best way to investigate its viability is to derive observable predictions which yield evidence or constraints for the model, when compared with actual observations. In this paper we derive the photon sphere and the perihelion shift for weak $f(T)$ perturbations of general relativity. We consistently calculate first order teleparallel perturbations of Schwarzschild and Mink

We propose a new model in the teleparallel framework where we consider a scalar field nonminimally coupled to both the torsion $T$ and a boundary term given by the divergence of the torsion vector $B=\frac{2}{e}{\ensuremath{\partial}}_{\ensuremath{\mu}}(e{T}^{\ensuremath{\mu}})$. This is inspired by the relation $R=\ensuremath{-}T+B$ between the Ricci scalar of general relativity and the torsion of teleparallel gravity. This theory in suitable limits incorporates both the nonminimal coupling of

Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to $|{c}_{g}/c\ensuremath{-}1|\ensuremath{\gtrsim}{10}^{\ensuremath{-}15}$. In this paper, we study the propagation of gravitational waves in a recently proposed model of Horndeski gravity in which its teleparallel gravity analog is formulated. As usually done in these analyses, we consider a flat cosmological background in which curvature is replaced by torsion as the expressi

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicit

Abstract The study of cosmological perturbation theory in f ( T ) gravity is a topic of great interest in teleparallel gravity since this is one of the simplest generalizations of the theory that modifies the teleparallel equivalent of general relativity. In this work, we explore the possibility of a non-flat FLRW background solution and perform perturbations for positively as well as negatively curved spatial geometries, together with a comparison to the flat case. We determine the generalized