Gravitational acceleration in a class of geometric sigma models

Abstract: In this work, I examine spherically symmetric solutions in geometric sigma models with four scalar fields. This class of models turns out to be a subclass of the wider class of scalar-vector-tensor theories of gravity. The purpose of the present study is to examine how the additional four degrees of freedom modify Newtonian gravitational acceleration. I have restricted my considerations to pointlike sources in de Sitter background. The resulting gravitational acceleration has the form of a power series, with four major terms standing out. The first and the second are the familiar Newtonian and MOND terms, which dominate at short distances. The third term is dominant at large distances. It is the $\Lambda$CDM term responsible for the accelerated expansion of the Universe. Finally, the fourth term provides an extra repulsive acceleration that grows exponentially fast with distance. This term becomes significant only at extremely large distances that go beyond the observable Universe. As for the time dependence of the calculated gravitational acceleration, it turns out to have nontrivial, oscillatory character.