Diffusive inflationary cosmology
The author considers the Ricci flow equation \(g'(t)=-2k Ric(g(t))+Dg(t)\) for a Riemannian metric g(t) on a compact 3-manifold, where k and D are some constants. This is related to general relativity by considering a corresponding Lorentzian metric \(^{(4)}g=-c^ 2dt^ 2+g(t).\) For metrics of this form, Einstein's vacuum field equation with cosmological constant reduces to a second order differential equation for g(t) along with two constraint equations. The main goal of the article is to show a long-time agreement of these two dynamical problems under additional assumptions which are of interest in connection with inflationary cosmology.
scientific article; zbMATH DE number 4209041