We study curved isotropic cosmologies filled with two interacting fluids near their time singularities. We find that a number of these universes asymptote to flat limits in the sense that their asymptotic properties become indistinguishable from those of flat Friedmann-Robertson-Walker models on approach to the singularity along any asymptotic direction. In particular, there are no essential singularities in these models. We discuss connections of this result with possible extensions of the cosmic no hair theorem to the case of two interacting fluids, and also provide links to a quantum cosmological treatment of real and complex Euclidean such solutions.

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to dete

We study the generic transport of slice energy between the scalar field generated by the conformal transformation of higher-order gravity theories and the matter component. We give precise relations for this exchange in the cases of dust and perfect fluids. We show that, unless we are in a stationary spacetime where slice energy is always conserved, in non-stationary situations, contributions to the total slice energy depend on whether or not test matter follows geodesics in both frame representations of the dynamics, that is, on whether or not the two conformally related frames are physically indistinguishable.