The Galactic Center as a laboratory for theories of gravity and dark matter.

The Galactic Center (GC) of the Milky Way, thanks to its proximity, allows to perform astronomical observations that investigate physical phenomena at the edge of astrophysics and fundamental physics. As such, it offers a unique laboratory to probe gravity, where one can not only test the basic predictions of general relativity (GR), but is also able to falsify theories that, over time, have been proposed to modify or extend GR; to test different paradigms of dark matter; and to place constraints on putative models that have been formulated as alternatives to the standard black hole paradigm in GR. In this review we provide a general overview of the history of observations of the GC, emphasizing the importance, in particular on the smallest-observable scales, that they had in opening a new avenue to improve our understanding of the underlying theory of gravity in the surrounding of a supermassive compact object.

Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole.

The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.

f(T) teleparallel gravity and cosmology.

Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T) gravity, where f (T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations-or, alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.

Modified gravity revealed along geodesic tracks.

The study of the dynamics of a two-body system in modified gravity constitutes a more complex problem than in Newtonian gravity. Numerical methods are typically needed to solve the equations of geodesics. Despite the complexity of the problem, the study of a two-body system in f(R) gravity leads to a new exciting perspective hinting the right strategy to adopt in order to probe modified gravity. Our results point out some differences between the semiclassical (Newtonian) approach, and the relativistic (geodesic) one thus suggesting that the latter represents the best strategy for future tests of modified theories of gravity. Finally, we have also highlighted the capability of forthcoming observations to serve as smoking gun of modified gravity revealing a departure from GR or further reducing the parameter space of f(R) gravity.

Noether symmetries in Gauss-Bonnet-teleparallel cosmology.

A generalized teleparallel cosmological model, [Formula: see text], containing the torsion scalar T and the teleparallel counterpart of the Gauss-Bonnet topological invariant [Formula: see text], is studied in the framework of the Noether symmetry approach. As [Formula: see text] gravity, where [Formula: see text] 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, [Formula: see text] contains all the possible information directly related to the torsion tensor. In this paper, we discuss how the Noether symmetry approach allows one to fix the form of the function [Formula: see text] and to derive exact cosmological solutions.