Effects of modified Chaplygin gas on structure formation in the universe

In this paper, the structure formation theories for the modified Chaplygin gas (MCG) model are established in the linear and non-linear regimes. Concretely, for the linear regime, the evolutions of the growth index \(f\) and the growth variable \(T\) are illustrated for the interacting MCG (IMCG) model and MCG model without interaction between dark energy and dark matter, which can give reasonable predictions for structure formation. While for the non-linear regime, by supposing the homogeneity and conservation of dark energy when the system reaches virialization, we can point out that MCG reaches the state of turn around later than GCG, the value of the collapse factor in MCG model is bigger than the fiducial value 0.5 in Einstein-de Sitter universe, namely \(\eta >0.5\), because of the effective repulsive force of dark energy, and the density contrast of the virialization tends to the Einstein-de Sitter value \(18\pi ^{2}\). Furthermore, the evolutions of the cluster number counts in LCDM, GCG and MCG models without and with interaction between dark energy and dark matter are illustrated by extending the Press-Schechter framework, which can exhibit the differences among the three models.