Reformulating scalar-tensor field theories as scalar-scalar field theories using a novel geometry.

In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, , on the cotangent bundle of a differentiable manifold . This will enable me to use the second vertical derivatives of , along with the differential of a scalar field on , to construct a Lorentzian metric on that depends upon . I refer to a field theory based upon a manifold with such a Lorentzian structure as a scalar-scalar field theory. We shall study such a theory when is chosen so that the resultant metric on has the form of a Friedmann-Lemaître-Robertson-Walker metric, and the Lagrangian has a particularly simple form. It will be shown that the scalar-scalar theory determined by the Lagrangian can generate self-inflating universes, which can be pieced together to form multiverses with non-Hausdorff topologies, in which the global time function multifurcates at  = 0. Some of the universes in these multiverses begin explosively, and then settle down to a period of much quieter accelerated expansion, which can be followed by a collapse to its original, pre-expansion state. This article is part of the theme issue 'The future of mathematical cosmology, Volume 1'.