On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)

TL;DR

This paper demonstrates that all torsion-free vacuum solutions in a de Sitter gauge theory of gravity are equivalent to solutions of Einstein's equations with a positive cosmological constant, extending to more general quadratic Lagrangians.

Contribution

It proves the equivalence of torsion-free vacuum solutions in de Sitter gauge gravity to Einstein solutions, including more general quadratic gravitational Lagrangians.

Findings

Torsion-free vacuum solutions match Einstein solutions with positive cosmological constant.

Equivalence holds for models with quadratic gravitational Lagrangian ($F^2+T^2$).

Results unify solutions across different gravitational theories.

Abstract

It is shown that all torsion-free vacuum solutions of the model of dS gauge theory of gravity are the vacuum solutions of Einstein field equations with the same positive cosmological constant. Furthermore, for the gravitational theories with more general quadratic gravitational Lagrangian ($F^2+T^2$), the torsion-free vacuum solutions are also the vacuum solutions of Einstein field equations.