General Relativity with a Positive Cosmological Constant <i>Λ</i> as a Gauge Theory

Abstract

In this paper, we show that the general relativity action (and Lagrangian) in recent Einstein⁻Palatini formulation is equivalent in four dimensions to the action (and Langrangian) of a gauge field. First, we briefly showcase the Einstein⁻Palatini (EP) action, and then we present how Einstein fields equations can be derived from it. In the next section, we study Einstein⁻Palatini action integral for general relativity with a positive cosmological constant Λ in terms of the corrected curvature Ω c o r . We see that in terms of Ω c o r this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω c o r .

Keywords

• action integral
• fiber bundle
• connection in a principal fiber bundle and its curvature
• pull-back of forms
• Lie groups and their algebras