The CMB spectrum in Cardassian models
  The dark energy in the Universe is described in the context of modified Friedmann equations as a fluid parameterized by the density of dark matter and undergoing an adiabatic expansion. This formulation is applied to the Cardassian model. Choosing then parameters consistent with the supernova observations, it gives a background expansion in which the cosmic temperature fluctuations are calculated. The resulting spectrum is quite similar to what is obtained in the standard concordance model. If the Cardassian fluid is interpreted as a new kind of interacting dark matter, its overdensities are driven into oscillations when the interaction energy is rising in importance. This does not occur in a description of the Cardassian fluctuations motivated by theories of modified gravity. There the energy of the underlying matter is also conserved, which requires appearance of effective shear stress in the late Universe. In both approaches that allow fluctuations the thermal power spectrum at large scales is much too strongly enhanced by the late integrated Sachs-Wolfe effect. With the interacting dark matter assumption, we conclude that the Cardassian model is ruled out by observations, expect in a small neighbourhood of the $\Lambda$CDM limit. 
Tomi Koivisto, Hannu Kurki-Suonio and Finn Ravndal