Cosmic acceleration is one of the most remarkable cosmological findings of recent years. Although a dark energy component has usually been invoked as the mechanism for the acceleration, a modification of the Friedmann equation from various higher dimensional models provides a feasible alternative. Cardassian expansion is one of these scenarios, in which the universe is flat, matter (and radiation) dominated, and accelerating but contains no dark energy component. This scenario is fully characterized by n, the power index of the so-called Cardassian term in the modified Friedmann equation, and Ωm, the matter density parameter of the universe. In this work, we first consider the constraints on the parameter space from the turnaround redshift, zq=0, at which the universe switches from deceleration to acceleration. We show that for every Ωm there exists a unique npeak(Ωm) that makes zq=0 reach its maximum value, (zq=0)max = exp [1/(2-3npeak)] - 1, which is nonlinearly inverse to Ωm. If the acceleration happens earlier than zq=0 = 0.6, as suggested by Type Ia supernovae measurements, we have Ωm 0.328 no matter what the power index is, and moreover, for reasonable matter density, Ωm ~ 0.3, it is found that n ~ (-0.45, 0.25). We next test this scenario using the Sunyaev-Zeldovich/X-ray data of a sample of 18 galaxy clusters with 0.14 z 0.83 compiled by Reese et al. We determine n and Ωm, as well as the Hubble constant H0, using the χ2 minimization method. The best fit to the data gives H0 = 59.2 km s-1 Mpc-1, n = 0.5, and Ωm = Ωb (Ωb is the baryonic matter density parameter). However, the constraints from the current Sunyaev-Zeldovich/X-ray data are weak, although a model with lower matter density is preferred. A certain range of the model parameters is also consistent with the data.
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