We reexamine the bending of light issue associated with the metric of the static, spherically symmetric solution of Weyl gravity discovered by Mannheim and Kazanas (1989). To this end we employ the procedure used recently by Rindler and Ishak to obtain the bending angle of light by a centrally concentrated spherically symmetric matter distribution in a Schwarzschild\char21{}de~Sitter background. In earlier studies the term $\gamma${}r in the metric led to the paradoxical result of a bending angle proportional to the photon impact parameter, when using the usual formalism appropriate to asymptotically flat space-times. However, employing the approach of light bending of Rindler and Ishak we show that the effects of this term are in fact insignificant, with the discrepancy between the two procedures attributed to the definition of the bending angle between the asymptotically flat and nonflat spaces.

In this work, we use a combined approach of Hubble parameter data together with redshift-space-distortion (fσ₈) data, which together are used to reconstruct the teleparallel gravity (TG) Lagrangian via Gaussian processes (GP). The adopted Hubble data mainly comes from cosmic chronometers, while for the Type Ia supernovae data we use the latest jointly calibrated Pantheon compilation. Moreover, we consider two main GP covariance functions, namely the squared-exponential and Cauchy kernels in order to show consistency (to within 1σ uncertainties). The core results of this work are the numerical reconstructions of the TG Lagrangian from GP reconstructed Hubble and growth data. We take different possible combinations of the datasets and kernels to illustrate any potential differences in this regard. We show that nontrivial cosmology beyond ΛCDM falls within the uncertainties of the reconstructions from growth data, which therefore indicates no significant departure from the concordance cosmological model.

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.

We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim and Kazanas [Astrophys. J. 342, 635 (1989)]. To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant $\Lambda$. We show that besides the general relativistic terms obtained earlier from the Schwarzschild–de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the linear term $\gamma r$ in the metric. Using data for perihelion shift observations, we obtain constraints on the value of the constant $\gamma$ similar to that obtained earlier using galactic rotational curves.