The Universality of vacuum Einstein equations with cosmological constant

It is shown that for a wide class of Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of so--called ``Palatini formalism'', i.e., treating the metric and the connection as independent variables, leads to Einstein equations. We discuss the role that the space of all such Lagrangians should play in better understanding this ``universality'' property of Einstein equations. As an example we investigate in detail the space of quadratic Lagrangians, where a bifurcation is shown to occur.

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