Tiago David Ferreira

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Abstract
Nonminimally coupled curvature-matter gravity models are an interesting alternative to the theory of general relativity 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 Schrodinger-Newton system. In nonlinear optics, the Schrodinger-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 nonminimal 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 static solutions arise even at low energy density regimes.

Abstract