Dark energy as a kinematic effect

Understand

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.