# Gravitational acceleration in a class of geometric sigma models

## TL;DR

This paper investigates how scalar fields in geometric sigma models alter gravitational acceleration, revealing modifications to Newtonian, MOND, and dark energy effects, including an exponentially growing repulsive term at vast distances.

## Contribution

It introduces a new class of solutions in geometric sigma models showing how additional scalar degrees of freedom modify gravitational acceleration with novel large-distance behavior.

## Key findings

- Newtonian and MOND terms dominate at short distances
- Lambda CDM term influences large-scale cosmic acceleration
- An exponentially growing repulsive acceleration appears at extremely large distances

## 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.