2017/03/16 by D. Herrera, I. Waga, Sérgio E. Jorás +1 · 3 citations
Mathematics · Physics and Astronomy · #Astrophysics #Bin #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Density contrast #Galaxies: Formation, Evolution, Phenomena #General relativity #Halo #Halo mass function #Mathematical physics #Mathematics #Metric (unit) #Omega #Physics #Quantum mechanics #Redshift #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.95.064029
published as Phys. Rev. D 95, 064029 (2017) · 11 pages, 6 figures, version accepted by Phys. Rev. D
arxiv created 2017/03/16 · openalex publication_date 2017/03/20 · arxiv updated 2017/03/22 · openalex created_date 2017/04/07 · openalex updated_date 2026/08/05
Critical overdensity \ensuremathδc is a key concept in estimating the number count of halos for different redshift and halo-mass bins, and therefore, it is a powerful tool to compare cosmological models to observations. There are currently two different prescriptions in the literature for its calculation, namely, the differential-radius and the constant-infinity methods. In this work we show that the latter yields precise results only if we are careful in the definition of the so-called numerical infinities. Although the subtleties we point out are crucial ingredients for an accurate determination of \ensuremathδc both in general relativity and in any other gravity theory, we focus on f(R)-modified gravity models in the metric approach; in particular, we use the so-called large (F=1/3) and small-field (F=0) limits. For both of them, we calculate the relative errors (between our method and the others) in the critical density \ensuremathδc, in the comoving number density of halos per logarithmic mass interval nlnM, and in the number of clusters at a given redshift in a given mass bin Nbin, as functions of the redshift. We have also derived an analytical expression for the density contrast in the linear regime as a function of the collapse redshift zc and \mathrm\ensuremathΩm0 for any F.