Abstract
Within the standard paradigm, dark energy is taken as a homogeneous fluid that drives the accelerated expansion of the universe and does not contribute to the mass of collapsed objects such as galaxies and galaxy clusters. The abundance of galaxy clusters—measured through a variety of channels—has been extensively used to constrain the normalization of the power spectrum: it is an important probe as it allows us to test if the standard ΛCDM model can indeed accurately describe the evolution of structures across billions of years. It is then quite significant that the Planck satellite has detected, via the Sunyaev-Zel'dovich effect, less clusters than expected according to the primary CMB anisotropies. One of the simplest generalizations that could reconcile these observations is to consider models in which dark energy is allowed to cluster, i.e., allowing its sound speed to vary. In this case, however, the standard methods to compute the abundance of galaxy clusters need to be adapted to account for the contributions of dark energy. In particular, we examine the case of clustering dark energy—a dark energy fluid with negligible sound speed—with a redshift-dependent equation of state. We carefully study how the halo mass function is modified in this scenario, highlighting corrections that have not been considered before in the literature. We address modifications in the growth function, collapse threshold, virialization densities and also changes in the comoving scale of collapse and mass function normalization. Our results show that clustering dark energy can impact halo abundances at the level of 10%–30%, depending on the halo mass, and that cluster counts are modified by about 30% at a redshift of unity.
Highlights
Background evolution and growth functionIn order to show the impact of DE fluctuations on the halo collapse, we adopt a DE with a linear parametrization of the equation of state, w = w0 + (1 − a) wa
Our results show that clustering dark energy can impact halo abundances at the level of 10%–30%, depending on the halo mass, and that cluster counts are modified by about 30% at a redshift of unity
In this work we carefully examine how the halo mass function is modified in the presence of clustering DE — a dark energy fluid with negligible sound speed — with a redshiftdependent equation of state, highlighting corrections that have not been considered in the literature before
Summary
The SC model can be generalized to treat fluids other than pressureless matter using the Pseudo-Newtonian Cosmology approach [19,20,21]. Where θ is the divergence of the peculiar velocity, δm = δρm/ρm and δde = δρde/ρde In this approach, the redshift of collapse, zc, is determined when δm → ∞, which is numerically implemented as certain threshold that reproduces the EdS results. The authors show that the numerical collapse threshold is not the same for different redshifts, which in turn generates a spurious increase of δc with z This can be corrected by calibrating the numerical threshold as a function of the redshift in order to reproduce some known δc and demanding that it approaches the EdS value at high-z. Once this calibration is done, we verified that both approaches give essentially the same results for the models under consideration in this work. The radial approach is more robust because it does not demand any redshiftdependent calibration and for this reason it will be used here
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