# General relativity with a positive cosmological constant $\lambda $ as a gauge theory

## TL;DR

This paper demonstrates that general relativity with a positive cosmological constant can be formulated as a gauge theory by expressing the Einstein-Palatini action in terms of a curvature form, providing a new geometric perspective.

## Contribution

It shows the equivalence of the Einstein-Palatini formulation of general relativity with a gauge field action, extending to positive cosmological constants and offering a geometric interpretation.

## Key findings

- Reformulation of Einstein-Palatini action as a gauge field action
- Derivation of Einstein equations from gauge-theoretic perspective
- Geometric interpretation of the curvature in the gauge formulation

## Abstract

In the paper we show that the general relativity action (and Lagrangian) in recent Einstein-Palatini formulation is equivalent to the action (and Langrangian) of a gauge field. We begin with a bit of information of the Einstein-Palatini (EP) action, then we present how Einstein fields equations can be derived from it. In the next section, we consider Einstein-Palatini action integral for general relativity with a positive cosmological constant $\Lambda $ in terms of $\hat{F}$, the curvature of the affine connection's pulled back from de Sitter bundle to Lorentz bundle. We will see that in terms of $\hat{F}$ this action takes the form typical for a gauge field. Finally, we give a geometrical interpretation of the curvature $\hat{F}$.