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.

We investigate the gravitational waves and their properties in various modified teleparallel theories, such as $f(T)$, $f(T,B)$, and $f(T,T_G)$ 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 $f(T,T_G)$ 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.

We investigate the four solar system tests of gravity—perihelion precession, light bending, Shapiro time delay, gravitational redshift—in $f(T)$ gravity. In particular, we investigate the solution derived by Ruggiero and Radicella, Phys. Rev. D 91, 104014 (2015). for a nondiagonal vierbein field for a polynomial $f(T)=T+\alpha T^n$, where $\alpha$ is a constant and $|n|\ne 1$. In this paper, we derive the solutions for each test, in which Weinberg’s, Bodenner and Will’s, Cattani et al., and Rindler and Ishak’s methods are applied, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972); Am. J. Phys. 71 (2003); Phys. Rev. D 87, 047503 (2013); Phys. Rev. D 76, 043006 (2007). We set a constraint on $\alpha$ for $n=2$, 3 by using data available from literature.

Teleparallel Gravity offers the possibility of reformulating gravity in terms of torsion by exchanging the Levi-Civita connection with the Weitzenböck connection which describes torsion rather than curvature. Surprisingly, Teleparallel Gravity can be formulated to be equivalent to general relativity for a appropriate setup. Our interest lies in exploring an extension of this theory in which the Lagrangian takes the form of f(T, B) where T and B are two scalars that characterize the equivalency with general relativity. In this work, we explore the possible of reproducing well-known cosmological bouncing scenarios in the flat Friedmann–Lemaître–Robertson–Walker geometry using this approach to gravity. We study the types of gravitational Lagrangians which are capable of reconstructing analytical solutions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce settings. These new cosmologically inspired models may have an effect on gravitational phenomena at other cosmological scales.

In this paper, we investigate the stability of the flat Friedmann-Lemaitre-Robertson-Walker metric in $f(T)$ gravity. This is achieved by analyzing the small perturbations, $\delta$ about the Hubble parameter and the matter energy density, ${\delta }_{\mathrm{m}}$. We find that $\delta \propto \dot{H}/H$ and ${\delta }_{\mathrm{m}}\propto H$. Since the Hubble parameter depends on the function $f(T)$, two models were considered (A) the power-law model $f(T)=\alpha (-T{)}^n$, and (B) the exponential model $f(T)=\alpha T_0(1-\exp [-p\sqrt{\frac{T}{T_0}}])$, where the parameters $n$ and $p$ were chosen to give comparable physical results. For the parameters considered, it was found that the solutions are stable with vanishing $\delta$ and decaying then constant ${\delta }_{\mathrm{m}}$, meaning that the matter perturbations persist during late times.

Gravitomagnetism characterizes phenomena in the weak-field limit within the context of rotating systems. These are mainly manifested in the geodetic and Lense-Thirring effects. The geodetic effect describes the precession of the spin of a gyroscope in orbit about a massive static central object, while the Lense-Thirring effect expresses the analogous effect for the precession of the orbit about a rotating source. In this work, we explore these effects in the framework of Teleparallel Gravity and investigate how these effects may impact recent and future missions. We find that teleparallel theories of gravity may have an important impact on these effects which may constrain potential models within these theories.