C-theory provides a unified framework to study metric, metric-affine and more general theories of gravity. In the vacuum weak-field limit of these theories, the parameterized post-Newtonian (PPN) parameters $beta$ and $gamma$ can differ from their ge
neral relativistic values. However, there are several classes of models featuring long-distance modifications of gravity but nevertheless passing the Solar system tests. Here it is shown how to compute the PPN parameters in C-theories and also in nonminimally coupled curvature theories, correcting previous results in the literature for the latter.
A canonic scalar field minimally coupled to a disformal metric generated by the field itself is considered. Causality and stability conditions are derived for such a field. Cosmological effects are studied and it is shown that the disformal modificat
ion could viably trigger an acceleration after a scaling matter era, thus possibly alleviating the coincidence problem.
We study the consequences of the $f(R/Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the correction ter
ms. The evolution of cosmological matter structures is shown to be governed by an effective time dependent Newtons constant. We also analyze the propagation of the perturbation modes. Tensor and vector modes are only slightly modified, but two new scalar degrees of freedom are present. Their causality and stability is demonstrated, and their formal ghost conditions are related to a singularity of the cosmological background. In general, the Newtonian limit of these models has no apparent conflicts with observations but can provide useful constraints.
We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the potential
minimum while dominant, or if driving an anisotropic expansion with nearly vanishing quadropole today. The Bianchi I model with a spatial field and an isotropic fluid is studied as a dynamical system, and several types of scaling solutions are found. On the other hand, time-like fields are automatically compatible with large-scale isotropy. We show that they can be dynamically important if non-minimal gravity couplings are taken into account. As an example, we reconstruct a vector-Gauss-Bonnet model which generates the concordance model acceleration at late times and supports an inflationary epoch at high curvatures. The evolution of vortical perturbations is considered.
