Signatures of kinetic gravity braiding in cosmological probes of the gravitational field

We study the observational signatures of kinetic gravity braiding (KGB) models in relativistic cosmological probes constructed along the past light cone. Using the relativistic N-body code KGB-evolution, we generate light-cone outputs and compute several observables that directly probe the gravitational field, including weak gravitational lensing convergence, Shapiro time delay, the integrated Sachs-Wolfe and Rees-Sciama (ISW-RS) effects, and gravitational redshift. Full-sky maps and angular power spectra of these quantities are constructed and compared with k-essence models and predictions from linear perturbation theory. We find that the derivative coupling between the scalar field and the metric modifies both the amplitude and the time evolution of the gravitational potentials, producing scale-dependent deviations ranging from a few percent to tens of percent. In particular, the ISW-RS signal exhibits the largest fractional response, as the slower decay of the Weyl potential suppresses the KGB signal in the ISW-dominated regime, whereas nonlinear evolution reverses this trend at higher multipoles, producing differences of tens of percent relative to k-essence. Weak gravitational lensing also provides a strong complementary probe and, for the model considered here, exhibits clear deviations from the k-essence prediction at small scales with enhancements up to about 10 - 12% at multipoles about 10 squared - 10 cubed. Our results show that linear perturbation theory accurately describes the large-scale behaviour, while nonlinear effects become important at smaller scales, particularly for the ISW-RS signal and, more moderately, for the convergence, and must therefore be included for reliable theoretical predictions.