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Generalized Cardassian Expansion: Models in Which the Universe is Flat, Matter Dominated, and Accelerating

The Cardassian universe is a proposed modification to the Friedmann Robertson Walker (FRW) equation in which the universe is flat, matter dominated, and accelerating. Here we generalize the original Cardassian proposal to include additional variants on the FRW equation. Specific examples are presented. In the ordinary FRW equation, the right hand side is a linear function of the energy density, $H^2 \sim ρ$. Here, instead, the right hand side of the FRW equation is a different function of the energy density, $H^2 \sim g(ρ)$. This function returns to ordinary FRW at early times, but modifies the expansion at a late epoch of the universe. The only ingredients in this universe are matter and radiation: in particular, there is {\it no} vacuum contribution. Currently the modification of the FRW equation is such that the universe accelerates. The universe can be flat and yet consist of only matter and radiation, and still be compatible with observations. The energy density required to close the universe is much smaller than in a standard cosmology, so that matter can be sufficient to provide a flat geometry. The modifications may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. The Cardassian model survives several observational tests, including the cosmic background radiation, the age of the universe, the cluster baryon fraction, and structure formation. As will be shown in future work, the predictions for observational tests of the generalized Cardassian models can be very different from generic quintessence models, whether the equation of state is constant or time dependent.