Imprints of dark energy on structure formation: No universality in mass functions?

In this proceedings for the invisible universe conference, we present our results on the imprints of dark energy on structure formation [4]. This article follows the one of Rasera et al. [10] which features the imprints of dark energy on the non linear power spectrum [2]. In this proceedings, we focus on the non linear imprints of dark energy on the mass functions and question the Jenkins et al. approximation of the universality of mass functions in the context of dark energies [6]. We first calculate the critical density formation threshold δ(z) and the overdensity detection parameter Δ(z) for dark energy cosmologies, using the spherical collapse model. We show that these non linear parameters keep a record of the history of the universe expansion and in particular that these parameters are quantitatively modified by the recent acceleration, driven by the dark energy. We show that the consequences on the mass functions should be detected in numerical simulations. In the second section, we present our dark energy models, the numerical setup and discuss the numerical checks that were necessary to guarantee a relevant precision for the purpose of detecting dark imprints on the mass functions. In the third section, we present our numerical results. We show that a different nature of the dark energy, or a variation of the quantity of dark energy in the universe, can lead to more than 20% deviations of mass functions to a universal behavior. We then quantitatively explain these deviations on the basis of the non linear parameters and give a parameterisation for the detection parameter that permits a unique prediction of the dark energy cosmologies mass functions up to a precision of 5% (Courtin et al. [4]). We finally conclude.