Cardassian Expansion: Dark Energy Density from Modified Friedmann   Equations
  The Cardassian universe is a proposed modification to the Friedmann equation in which the universe is flat, matter dominated, and accelerating. In the ordinary Friedmann equation, the right hand side is a linear function of the energy density, $H^2 \sim \rho$. Here, instead, the right hand side of the Friedmann equation is a different function of the energy density, $H^2 \sim g(\rho)$. This function returns to ordinary Friedmann at early times, but drives acceleration of the universe at the current epoch. The only ingredients in this universe are matter and radiation: in particular, there is NO vacuum contribution. The new term required may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. A second possible interpretation of Cardassian expansion is developed, in which we treat the modified Friedman equations as due to a fluid, in which the energy density has new contributions with negative pressure (possibly due to dark matter with self-interactions). Predictions are shown for observational tests of generalized Cardassian models in future supernova surveys. 
Katherine Freese