Abstract. We present an extension of f (T ) gravity, allowing for a general coupling of the torsion scalar T with the trace of the matter energy-momentum tensor T . The resulting f (T, T ) theory is a new modified gravity, since it is different from all the existing torsion or curvature based constructions. Applied to a cosmological framework, it leads to interesting phenomenology. In particular, one can obtain a unified description of the initial inflationary phase, the subsequent non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase. Additionally, the effective dark energy sector can be quintessence or phantom-like, or exhibit the phantom-divide crossing during the evolution. Moreover, in the far future the universe results either to a de Sitter exponential expansion, or to eternal power-law accelerated expansions. Finally, a detailed study of the scalar perturbations at the linear level reveals that f (T, T ) cosmology can be free of ghosts and instabilities for a wide class of ansatzes and model parameters.

We construct an extension of f (T ) gravity with the inclusion of a non-minimal torsion-matter coupling in the action. The resulting theory is a novel gravitational modification, since it is different from both f (T ) gravity, as well as from the nonminimal curvature-matter-coupled theory. The cosmological application of this new theory proves to be very interesting. In particular, we obtain an effective dark energy sector whose equation-of-state parameter can be quintessence-or phantom-like, or exhibit the phantom-divide crossing, while for a large range of the model parameters the universe results in a de Sitter, dark-energy-dominated, accelerating phase. Additionally, we can obtain earlytime inflationary solutions too, and thus provide a unified description of the cosmological history.PACS numbers: 04.50. Kd, 95.36.+x

It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found.Here we consider a model in which the non-minimal coupling is ruled by a dynamically changingan arbitrary function of the scalar field φ. It is shown that in this case the existence of scaling attractors is possible, which means that the universe will eventually enter these scaling attractors, regardless of the initial conditions. As a consequence, the cosmological coincidence problem could be alleviated without fine-tunings.arXiv:1305.0474v2 [gr-qc]

A detailed dynamical analysis of the tachyonic teleparallel dark energy model, in which a non-canonical scalar field (tachyon field) is non-minimally coupled to gravitation, is performed. It is found that, when the non-minimal coupling is ruled by a dynamically changing coefficient $\alpha\equiv f_{,\phi}/\sqrt{f}$, with $f(\phi)$ an arbitrary function of the scalar field $\phi$, the universe may experience a field-matter-dominated era "$\phi$MDE", in which it has some portions of the energy density of $\phi$ in the matter dominated era. This is the most significant difference in relation to the so-called teleparallel dark energy scenario, in which a canonical scalar field (quintessence) is non-minimally coupled to gravitation.Comment: 14 pages, 1 figure. arXiv admin note: text overlap with arXiv:1305.047

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We construct $F(T,\left(\nabla{T}\right)^2,\Box {T})$ gravitational modifications, which are novel classes of modified theories arising from higher-derivative torsional terms in the action, and are different than their curvature analogue. Applying them in a cosmological framework we obtain an effective dark energy sector that comprises of the novel torsional contributions. We perform a detailed dynamical analysis for two specific examples, extracting the stable late-time solutions and calculating the corresponding observables. We show that the thermal history of the universe can be reproduced, and it can result in a dark-energy dominated, accelerating universe, where the dark-energy equation-of-state parameter lies in the quintessence regime, or may exhibit the phantom-divide crossing during the cosmological evolution. Finally, the scale factor behaves asymptotically either as a power-law or as an exponential, in agreement with observations.Comment: 13 pages, 6 figures, 2 Tables, version published in PR

In this work, we perform a detailed dynamical analysis for the cosmological applications of a nonminimal torsion-matter coupled gravity. Two alternative formalisms are proposed, which enables one to choose between the easier approach for a given problem, and furthermore, we analyze six specific models. In general, we extract fixed points corresponding either to dark-matter dominated, scaling decelerated solutions, or to dark-energy dominated accelerated solutions. Additionally, we find that there is a small parameter region in which the model can experience the transition from matter epoch to dark-energy era. These feature are in agreement with the observed universe evolution, and make the theory a successful candidate for the description of Nature.PACS numbers: 04.50. Kd, 95.36.+x

It is investigated the cosmological dynamics of scalar-torsion $$f(T,\phi )$$ f ( T , ϕ ) gravity as a dark energy model, where T is the torsion scalar of teleparallel gravity and $$\phi $$ ϕ is a canonical scalar field. In this context, we are concerned with the phenomenology of the class of models with non-linear coupling to gravity and exponential potential. We obtain the critical points of the autonomous system, along with the stability conditions of each one of them and their cosmological properties. Particularly, we show the existence of new attractors with accelerated expansion, as well as, new scaling solutions in which the energy density of dark energy scales as the background fluid density, thus, defining the so-called scaling radiation and scaling matter epochs. The scaling solutions are saddle points, and therefore, the system exits these solutions to the current epoch of cosmic acceleration, towards an attractor point describing the dark energy-dominated era.