General relativity with a positive cosmological constant \(\lambda\) as a gauge theory (Q2306144)

Summary: 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 \(\Lambda\) in terms of the corrected curvature \(\Omega_{\mathrm{cor}}\). We see that in terms of \(\Omega_{\mathrm{cor}}\) this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the corrected curvature \(\Omega_{\mathrm{cor}}\).