Tachyonic Universes in Patch Cosmologies with $\Omega>1$
  In this article we study closed inflationary universe models by means of a tachyonic field. We described a general treatment for created a universe with $\Omega>1$ in patch cosmology, which is able to represent General Relativity, Gauss-Bonnet or Randall-Sundrum patches. We use recent data from astronomical observations to constrain the parameters appearing in our model. 
Sergio del Campo, Ramon Herrera, Pedro Labrana, Carlos Leiva and Joel   Saavedra