Kaluza--Klein-type models of de Sitter and Poincar\'e gauge theories of gravity

TL;DR

This paper develops Kaluza--Klein-type models for de Sitter and Poincaré gauge theories of gravity, providing a gauge-invariant formalism that incorporates a cosmological term and reduces to general relativity under certain conditions.

Contribution

It introduces a novel gauge-invariant formalism for Kaluza--Klein-type gravity models with cosmological terms, extending previous models and including variable cosmological terms.

Findings

A gauge-invariant formalism for de Sitter and Minkowski bundles.

Models recover general relativity with a cosmological term in specific limits.

Inclusion of variable cosmological terms in the models.

Abstract

We construct Kaluza--Klein-type models with a de Sitter or Minkowski bundle in the de Sitter or Poincar\'e gauge theory of gravity, respectively. A manifestly gauge-invariant formalism has been given. The gravitational dynamics is constructed by the geometry of the de Sitter or Minkowski bundle and a global section which plays an important role in the gauge-invariant formalism. Unlike the old Kaluza--Klein-type models of gauge theory of gravity, a suitable cosmological term can be obtained in the Lagrangian of our models and the models in the spin-current-free and torsion-free limit will come back to general relativity with a corresponding cosmological term. We also generalize the results to the case with a variable cosmological term.