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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]

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]