Constraining Generalized Non-local Cosmology from Noether Symmetries

We study a generalized nonlocal 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 are needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to by introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de-Sitter and power law cosmological solutions for different nonlocal theories. The symmetries for the generalized non-local theory is also found and some cosmological solutions are also achieved under the full theory.Comment: 15 pages, to be published in Eur.Phys.J.

Can Horndeski Theory be recast using Teleparallel Gravity?

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. In this paper, we study the analogue of Horndeski's theory in the teleparallel gravity framework were gravity is mediated through torsion instead of curvature. We show that, even though, many terms are the same as in the curvature case, we have much richer phenomenology in the teleparallel setting because of the nature of the torsion tensor. Moreover, Teleparallel Horndenski contains the standard Horndenski gravity as a subcase and also contains many modified Teleparallel theories considered in the past, such as $f(T)$ gravity or Teleparallel Dark energy. Thus, due to the appearing of a new term in the Lagrangian, this theory can explain dark energy without a cosmological constant, may describe a crossing of the phantom barrier, explain inflation and also solve the tension for $H_0$, making it a good candidate for a correct modified theory of gravity.Comment: 18 pages, 1 figur

Noether Symmetries in Gauss-Bonnet-teleparallel cosmology

A generalized teleparallel cosmological model, $f(T_\mathcal{G},T)$, containing the torsion scalar $T$ and the teleparallel counterpart of the Gauss-Bonnet topological invariant $T_{\mathcal{G}}$, is studied in the framework of the Noether Symmetry Approach. As $f(\mathcal{G}, R)$ gravity, where $\mathcal{G}$ is the Gauss-Bonnet topological invariant and $R$ is the Ricci curvature scalar, exhausts all the curvature information that one can construct from the Riemann tensor, in the same way, $f(T_\mathcal{G},T)$ contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether Symmetry Approach allows to fix the form of the function $f(T_\mathcal{G},T)$ and to derive exact cosmological solutions.Comment: 6 page

Noether Symmetries as a geometric criterion to select theories of gravity

We review the {\it Noether Symmetry Approach} as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.Comment: 16 pages, accepted for publication in the International Journal of Geometric Methods in Modern Physic

Reviving Horndeski Theory using Teleparallel Gravity after GW170817

Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to $|c_{g}/c-1|\gtrsim 10^{-15}$. In this Letter we study the tensorial perturbations in a flat cosmological background for an analogue version of Horndenki gravity which is based in Teleparallel Gravity constructed from a flat manifold with a nonvanishing torsion tensor. It is found that in this approach, one can construct a more general Horndeski theory satisfying $c_T=c_g/c=1$ without eliminating the coupling functions $G_5(\phi,X)$ and $G_4(\phi,X)$ that were highly constrained in standard Horndeski theory. Hence, in the Teleparallel approach one is able to restore these terms, creating an interesting way to revive Horndeski gravity.Comment: 12 pages, 0 figure