The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

No abstract

Equation of State LHS Left hand side RHS Right hand side STEGR Symmetric teleparallel equivalent of general relativity TEGB Teleparallel equivalent of the Gauss-Bonnet PPN Parameterized post-Newtonian formalism SN Supernova (we use abbreviations SNeIa and SNIa to refer to supernova type 1a) BAO Baryonic Acoustic Oscillations CC Cosmic Chronometers DE Dark energy HDE Holographic Dark Energy QCD Quantum Chromodynamics PlDE Pilgrim Dark Energy CMB Cosmic Microwave Background WMAP Wilkinson Microwave Anisotropy Probe SVT Scalar-Vector-Tensor VLBI Very Long Baseline Interferometry SH0ES Supernova H0 for the Equation of State TRGB Tip of the red-giant branch TDCOSMO Time-delay Cosmography vi

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, 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 Horndeski contains the standard Horndeski 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 appearance 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 H0, making it a good candidate for a correct modified theory of gravity.

General Relativity and the ΛCDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications.All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature.We list the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research.

No abstract

We investigate the gravitational waves and their properties in various modified teleparallel theories, such as f (T ), f (T, B) and f (T, TG) gravities. We perform the perturbation analysis both around a Minkowski background, as well as in the case where a cosmological constant is present, and for clarity we use both the metric and tetrad language. For f (T ) gravity we verify the result that no further polarization modes comparing to general relativity are present at first-order perturbation level, and we show that in order to see extra modes one should look at third-order perturbations.For non-trivial f (T, B) gravity, by examining the geodesic deviation equations, we show that extra polarization models, namely the longitudinal and breathing modes, do appear at first-order perturbation level, and the reason for this behavior is the fact that although the first-order perturbation does not have any effect on T , it does affect the boundary term B. Finally, for f (T, TG) gravity we show that at first-order perturbations the gravitational waves exhibit the same behavior to those of f (T ) gravity. Since different modified teleparallel theories exhibit different gravitational wave properties, the advancing gravitational-wave astronomy would help to alleviate the degeneracy not only between curvature and torsional modified gravity but also between different subclasses of modified teleparallel gravities.

No abstract