Constraints on Cardassian Scenario from the Expansion Turnaround Redshift and the Sunyaev-Zeldovich/X-ray Data

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 Friedmann equation from various higher dimensional models provides a feasible alternative. Cardassian expansion is one of these scenarios. In this work, we first consider the constraints on the parameter space from the turnaround redshift, z_{q=0}, at which the universe switches from deceleration to acceleration. We show that, for every Omega_m, there exist a unique n_{peak} (Omega_m), which makes z_{q=0} reach its maximum value, [z_{q=0}]_{max} = exp[1/ (2-3n_{peak})] -1, which is unlinearly inverse to Omega_m. If the acceleration happans earlier than z_{q=0} = 0.6, suggested by Type Ia supernovae measurements, we have Omega_m < 0.328 no matter what the power index is, and moreover, for reasonable matter density, Omega_m ~ 0.3, it is found 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. (2002). The constraints from the current SZ/X-ray data is weak, though a model with lower matter density is prefered. A certain range of the model parameters is also consistent with the data.