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.

We study the viability conditions for the absence of ghost, gradient and tachyonic instabilities, in scalar-torsion f(T,ϕ) gravity theories in the presence of a general barotropic perfect fluid. To describe the matter sector, we use the Sorkin-Schutz action and then calculate the second order action for scalar perturbations. For the study of ghost and gradient instabilities, we found that the gravity sector keeps decoupled from the matter sector and then applied the viability conditions for each one separately. Particularly, we verified that this theory is free from ghost and gradient instabilities, obtaining the standard results for matter, and for the gravity sector we checked that the corresponding speed of propagation satisfies c_s,g²=1. On the other hand, in the case of tachyonic instability, we obtained the general expressions for the mass eigenvalues and then evaluated them in the scaling matter fixed points of a concrete model of dark energy. Thus, we found a space of parameters where it is possible to have a stable configuration respecting the constraints from the CMB measurements and the BBN constraints for early dark energy. Finally, we have numerically corroborated these results by solving the cosmological equations for a realistic cosmological evolution with phase space trajectories undergoing scaling matter regimes, and then showing that the system presents a stable configuration throughout cosmic evolution.

It is investigated the reconstruction during the slow-roll inflation in the most general class of scalar-torsion theories whose Lagrangian density is an arbitrary function $$f(T,\phi )$$f ( T , ϕ ) of the torsion scalar T of teleparallel gravity and the inflaton $$\phi $$ϕ . For the class of theories with Lagrangian density $$f(T,\phi )=-M_{pl}^{2} T/2 - G(T) F(\phi ) - V(\phi )$$f ( T , ϕ ) = - M pl 2 T / 2 - G ( T ) F ( ϕ ) - V ( ϕ ) , with $$G(T)\sim T^{s+1}$$G ( T ) ∼ T s + 1 and the power s as constant, we consider a reconstruction scheme for determining both the non-minimal coupling function $$F(\phi )$$F ( ϕ ) and the scalar potential $$V(\phi )$$V ( ϕ ) through the parametrization (or attractor) of the scalar spectral index $$n_{s}(N)$$n s ( N ) and the tensor-to-scalar ratio r(N) as functions of the number of $$e-$$e - folds N. As specific examples, we analyze the attractors $$n_{s}-1 \propto 1/N$$n s - 1 ∝ 1 / N and $$r\propto 1/N$$r ∝ 1 / N , as well as the case $$r\propto 1/N (N+\gamma )$$r ∝ 1 / N ( N + γ ) with $$\gamma $$γ a dimensionless constant. In this sense and depending on the attractors considered, we obtain different expressions for the function $$F(\phi )$$F ( ϕ ) and the potential $$V(\phi )$$V ( ϕ ) , as also the constraints on the parameters present in our model and its reconstruction.

We study the evolution of cosmological perturbations around a homogeneous and isotropic background in the framework of the non-minimal torsion-matter coupling extension of f( T) gravity. We are...

We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian instability. In order for the black hole solutions to be stable, we study their generalized ‘Regge–Wheeler potential’. It turns out that the problem is reduced to an algebraic problem where three functions characterizing the black hole should be positive outside the horizon to prove the stability. We found that these conditions are similar to the no-ghost and Laplacian instability conditions. We apply our results to various known solutions.