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.

• Received 26 October 2018

DOI:https://doi.org/10.1103/PhysRevD.100.044008