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Conformal symmetries appear in many parts of physics and play a unique role in exploring the Universe. We consider the possibility of constructing conformal theories of gravity in the symmetric teleparallel gravity framework, where gravitation is expressed through nonmetricity rather than curvature or torsion. We demonstrate that it is possible to formulate a family of conformal theories with second-order field equations and have the metric tensor as the fundamental variable. Moreover, we consider the addition of a scalar field to the theory, and compare the results to the teleparallel gravity setting. Finally, we present the scalar-tensor representation of modified symmetric teleparallel theories, and among others we show that there is an interesting subcase that has the possibility of playing the role of dark energy. [ABSTRACT FROM AUTHOR]

Horndeski gravity was highly constrained from the recent gravitational wave observations by the LIGO Collaboration down to |cg/câ'1|â10â'15. In this paper, we study the propagation of gravitational waves in a recently proposed model of Horndeski gravity in which its teleparallel gravity analog is formulated. As usually done in these analyses, we consider a flat cosmological background in which curvature is replaced by torsion as the expression of gravitation. It is found that in this approach, one can construct a more general Horndeski theory satisfying cT=cg/c=1 without eliminating the coupling functions G5(Ï•,X) and G4(Ï•,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. In this way, we retain the original spirit of Horndeski gravity (unlike beyond Horndeski theories) while only changing the form in which the geometry of gravitation is expressed. [ABSTRACT FROM AUTHOR]

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 and in the case where a cosmological constant is present, and for clarity we use both the metric and the tetrad languages. 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 nontrivial 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 as 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. [ABSTRACT FROM AUTHOR]

Gravitational waves (GWs) have opened a new window on fundamental physics in a number of important ways. The next generation of GW detectors may reveal more information about the polarization structure of GWs. Additionally, there is growing interest in theories of gravity beyond general relativity (GR). One such theory which remains viable within the context of recent measurements of the speed of propagation of GWs is the teleparallel analog of Horndeski gravity. In this work, we explore the polarization structure of this newly proposed formulation of Horndeski theory. In curvature-based gravity, Horndeski theory is almost synonymous with extensions to GR since it spans a large portion of these possible extensions. We perform this calculation by taking perturbations about a Minkowski background and consider which mode propagates. The result is that the polarization structure depends on the choice of model parameters in the teleparallel Horndeski Lagrangian with a maximum of seven propagating degrees of freedom. While the curvature-based Horndeski results follows as a particular limit within this setup, we find a much richer structure of both massive and massless cases which produce scalar-vector-tensor propagating degrees of freedom. We also find that the GW polarization that emerges from the teleparallel analog of Horndeski gravity results in analogous massive and massless modes which take on at most four polarizations in the massless sector and two scalar ones in the massive sector. In none of the cases do we find vector polarizations. [ABSTRACT FROM AUTHOR]

Symmetric teleparallel gravity (STG) offers an interesting avenue to formulate a theory of gravitation that relies neither on curvature nor torsion but only on nonmetricity Q. Given the growing number of confirmed observations of gravitational waves (GWs) and their use to explore gravitational theories, in this work we investigate the GWs in various extensions of STG, focusing on their speed and polarization. We explore the plethora of theories that this new framework opens up, that is, as general relativity can be modified, so can the symmetric teleparallel equivalent of general relativity (STEGR). In this work, we investigate the fate of GWs in the generalized irreducible decomposition of STEGR, generalizations of the STEGR Lagrangian, f(Q), a scalar field nonminimally coupled to the STEGR Lagrangian, and the general setup of f(Q,B) theory where B is the boundary term difference between the Ricci scalar and the STEGR Lagrangian. Coincidentally, f(Q,B) forms a more general theory than f(R) gravity since Q embodies the second-order elements of the Ricci scalar while B takes on its fourth-order boundary terms. Our work deals mainly with the resulting scalar-vector-tensor polarization modes of the plethora of STG theories, and how they effect their respective speeds of propagation. [ABSTRACT FROM AUTHOR]