Non-Linear Lagrangians and Cosmological Theory

In relativistic cosmology the theory of uniform model universes is based on Einstein's equations, which derive from a variational principle the field-Lagrangian L of which is the scalar curvature R to within an arbitrary additive constant. In this work the possibility of taking L to be a more general invariant of the Riemann tensor is contemplated. The consequences of choosing L to be a function ϕ of R alone are tentatively examined under specialized circumstances, with particular attention to an open world-model oscillating between non-singular states. Difficulties revolving about the actual form which ϕ might take are discussed.