Abstract
Critical overdensity 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 both in general relativity and in any other gravity theory, we focus on -modified gravity models in the metric approach; in particular, we use the so-called large () and small-field () limits. For both of them, we calculate the relative errors (between our method and the others) in the critical density , in the comoving number density of halos per logarithmic mass interval , and in the number of clusters at a given redshift in a given mass bin , 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 and for any .
- Received 19 December 2016
DOI:https://doi.org/10.1103/PhysRevD.95.064029
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