In the Cardassian model , dark energy density arises from modifications to the Friedmann equation , which becomes H ^ { 2 } = g ( \rho _ { M } ) , where g ( \rho _ { M } ) is a new function of the energy density .
The universe is flat , matter dominated , and accelerating .
The distance redshift relation predictions of generalized Cardassian models can be very different from generic quintessence models , and can be differentiated with data from upcoming pencil beam surveys of Type Ia Supernovae such as SNAP .
We have found the interesting result that , once \Omega _ { m } is known to 10 % accuracy , SNAP will be able to determine the sign of the time dependence of the dark energy density .
Knowledge of this sign ( which is related to the weak energy condition ) will provide a first discrimination between various cosmological models that fit the current observational data ( cosmological constant , quintessence , Cardassian expansion ) .
Further , we have performed Monte Carlo simulations to illustrate how well one can reproduce the form of the dark energy density with SNAP .

To be concrete we study a class of two parameter ( n , q ) generalized Cardassian models that includes the original Cardassian model ( parametrized by n only ) as a special case .
Examples are given of MP Cardassian models that fit current supernovae and CMB data , and prospects for differentiating between MP Cardassian and other models in future data are discussed .
We also note that some Cardassian models can satisfy the weak energy condition w > -1 even with a dark energy component that has an effective equation of state w _ { X } < -1 .