2017/08/31 by Francesco Pace, Sven Meyer, Matthias Bartelmann · 1 citation
Physics and Astronomy · #Cluster analysis #Cosmology and Gravitation Theories #Dark energy #Extrapolation #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Inverse #Numerical integration #Robustness (evolution) #Statistical Mechanics and Entropy #Work (physics) #astro-ph.CO
paper · pdf · doi:10.1088/1475-7516/2017/10/040
33 pages, 8 figures. Version matching the published paper. Few more references with respect to the previous version
openalex created_date 2017/08/17 · openalex publication_date 2017/10/25 · arxiv created 2017/12/20 · arxiv updated 2017/12/21 · openalex updated_date 2026/08/06
In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δ c , which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ c for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.