Quasi-geodesics in relativistic gravity

TL;DR

This paper explores the concept of quasi-geodesics in relativistic gravity, focusing on how four-forces aligned with particle trajectories affect motion, with applications in cosmology and scalar-tensor theories.

Contribution

It introduces the idea of quasi-geodesics in relativistic gravity and discusses their implications in cosmological models involving pressure gradients and scalar fields.

Findings

Four-force parallel to particle trajectories can be eliminated via affine parametrization.

Affine parameter differs from proper time in such scenarios.

Applications include cosmology with pressure gradients and scalar-tensor theories.

Abstract

A four-force parallel to the trajectory of a massive particle can always be eliminated by going to an affine parametrization, but the affine parameter is different from the proper time. The main application is to cosmology, in which elements of the cosmic fluid are subject to a pressure gradient parallel to their four-velocities. Natural implementations of parallel four-forces occur when the particle mass changes and in scalar-tensor cosmology.