Constraints on the 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, zₐ=₀, at which the universe switches from deceleration to acceleration. We show that, for every Omegaₘ, there exist a unique n₏₄₀₊ (Omegaₘ), which makes zₐ=₀ reach its maximum value, zₐ=₀₌₀ₗ = exp1/ (2-3n₏₄₀₊) -1, which is unlinearly inverse to Omegaₘ. If the acceleration happans earlier than zₐ=₀ = 0. 6, suggested by Type Ia supernovae measurements, we have Omegaₘ < 0. 328 no matter what the power index is, and moreover, for reasonable matter density, Omegaₘ ~ 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.