Dark energy as a kinematic effect

TL;DR

This paper generalizes teleparallel gravity to include a dynamic cosmological function within a de Sitter-Cartan geometry, linking dark energy to local spacetime kinematics and proposing a novel theoretical framework.

Contribution

It introduces a de Sitter-regulated teleparallel gravity with a dynamic cosmological function that influences local spacetime kinematics, extending previous models.

Findings

The cosmological function has its own dynamics.

Dark energy affects local spacetime kinematics.

The theory is consistent with de Sitter symmetry.

Abstract

We present a generalization of teleparallel gravity that is consistent with local spacetime kinematics regulated by the de Sitter group $SO(1,4)$. The mathematical structure of teleparallel gravity is shown to be given by a nonlinear Riemann-Cartan geometry without curvature, which inspires us to build the generalization on top of a de Sitter-Cartan geometry with a cosmological function. The cosmological function is given its own dynamics and naturally emerges nonminimally coupled to the gravitational field in a manner akin to teleparallel dark energy models or scalar-tensor theories in general relativity. New in the theory here presented, the cosmological function gives rise to a kinematic contribution in the deviation equation for the world lines of adjacent free-falling particles. While having its own dynamics, dark energy manifests itself in the local kinematics of spacetime.