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We investigate the problem of finding a pure spin-connection formulation ofGeneral Relativity with non-vanishing cosmological constant. We first revisitthe problem at the linearised level and find that the pure spin-connection,quadratic Lagrangian, takes a form reminiscent to Weyl gravity, given by thesquare of a Weyl-like tensor. Upon Hodge dualisation, we show that the dualgauge field in (A)dS$_D$ transforms under $GL(D)$ in the same representation asa massive graviton in the flat spacetime of the same dimension. We give adetailed proof that the physical degrees of freedom indeed correspond to amassless graviton propagating around the (anti-) de Sitter background andfinally speculate about a possible nonlinear pure-connection theory dual toGeneral Relativity with cosmological constant.

A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS