Dynamical quintessence fields Press-Schechter mass function: detectability and effect on dark haloes

We present an investigations on the influence of dynamical quintessence field models on the formation of non-linear structures. In particular, we focus on the structure traced by the mass function. Our contribution builds on previous studies by considering two potentials not treated previousy and investigating the impact of the free parameters of two other models. Our approach emphasises the physical insight into the key role of the evolution of the equation of state. We use the variations in the spherical non-linear collapse caused by quintessence as a function of the model's potential in a Press Schechter scheme to obtain the differences in halo mass functions. The comparison is also done with the more usual scenario $\Lambda$CDM. We conclude the method should be promissing for discrimination using cluster mass determination and that the key role lies within the evolution of the equation of state.