General relativity with a positive cosmological constant Λ 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 cor . We see that in terms of Ω cor this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω cor .