Constraining the Schwarzschild–de Sitter solution in models of modified gravity

The Schwarzschild–de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f\left(R\right)$ and $f\left(T\right)$ theories, dRGT massive gravity, and Hořava–Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.