Pressureless stationary solutions in a Newton-Yukawa gravity model

Non-minimally coupled curvature-matter gravity models are an interesting alternative to the Theory of General Relativity and to address the dark energy and dark matter cosmological problems. These models have complex field equations that prevent a full analytical study. Nonetheless, in a particular limit, the behavior of a matter distribution can, in these models, be described by a Schr\"odinger-Newton system. In nonlinear optics, the Schr\"odinger-Newton system can be used to tackle a wide variety of relevant situations and several numerical tools have been developed for this purpose. Interestingly, these methods can be adapted to study General Relativity problems as well as its extensions. In this work, we report the use of these numerical tools to study a particular non-minimal coupling model that introduces two new potentials, an attractive Yukawa potential and a repulsive potential proportional to the energy density. Using the imaginary-time propagation method we have shown that stationary solutions arise even at low energy density regimes.