Dark energy as a kinematic effect

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.

6 pages, conclusions updated, references added

References in corpus (5)

• The teleparallel equivalent of general relativity
• Modified gravity models of dark energy
• de Sitter special relativity
• On the spacetime connecting two aeons in conformal cyclic cosmology
• Cartan geometry of spacetimes with a nonconstant cosmological function $\Lambda$

Cited by in corpus (9)

• Teleparallel Gravity: From Theory to Cosmology
• Model-independent reconstruction of $f(T)$ teleparallel cosmology
• General relativity as an attractor for scalar-torsion cosmology
• Reconstruction of $f(T)$-gravity in the absence of matter
• Modified teleparallel gravity with higher-derivative torsion terms
• Transitioning scenario of Bianchi-I universe within $f\left(R,T\right)$ formalism
• Interacting Quintessence in a New Scalar-Torsion Gravity
• Scale-invariant cosmology in de Sitter gauge theory
• A first-order approach to conformal gravity