Related papers: Perturbation theory and excursion set estimates of…
The excursion set theory based on spherical or ellipsoidal gravitational collapse provides an elegant analytic framework for calculating the mass function and the large-scale bias of dark matter haloes. This theory assumes that the…
We use the physics of ellipsoidal collapse to model the probability distribution function of the smoothed dark matter density field in real and redshift space. We provide a simple approximation to the exact collapse model which shows…
In this paper I consider the nonlinear evolution of a rare density fluctuation in a random density field with Gaussian fluctuations, and I rigorously show that it follows the spherical collapse dynamics applied to its mean initial profile.…
We present an analytical model for the non-spherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the…
We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
The Press--Schechter, excursion set approach allows one to make predictions about the shape and evolution of the mass function of bound objects. It combines the assumption that objects collapse spherically with the assumption that the…
We combine the physics of the ellipsoidal collapse model with the excursion set theory to study the shapes of dark matter halos. In particular, we develop an analytic approximation to the nonlinear evolution that is more accurate than the…
The excursion set approach is a framework for estimating how the number density of nonlinear structures in the cosmic web depends on the expansion history of the universe and the nature of gravity. A key part of the approach is the…
Recent analytical work on the modelling of dark halo abundances and clustering has demonstrated the advantages of combining the excursion set approach with peaks theory. We extend these ideas and introduce a model of excursion set peaks…
We present a new algorithm to sample the constrained eigenvalues of the initial shear field associated with Gaussian statistics, called the `peak/dip excursion-set-based' algorithm, at positions which correspond to peaks or dips of the…
The excursion set model provides a convenient theoretical framework to derive dark matter halo abundances. This paper generalizes the model by introducing a more realistic merging and collapse process. A new parameter regulates the…
Using the spherical collapse approach, we investigate the impact of two alternative dark matter models, each characterized by distinct non-zero equations of state, one constant and the other time dependent on the nonlinear regime.…
Collapse of the wave function appears to violate the quantum superposition principle as well as deterministic evolution. Objective collapse models propose a dynamical explanation for this phenomenon, by making a stochastic non-unitary and…
The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the nonlinear processes of collapse and…
We extend the evolution mapping approach, originally proposed by Sanchez (2022) to describe non-linear matter density fluctuations, to statistics of the cosmic velocity field. This framework classifies cosmological parameters into shape…
We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model…
Perturbation theory makes it possible to calculate the probability distribution function (PDF) of the large scale density field in the small variance limit. For top hat smoothing and scale-free Gaussian initial fluctuations, the result…
Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large scale structure of the Universe. In Papers I & II of this series we saw that the Spherical Collapse (SC) model…
We study the nonlinear evolution of matter overdensities using the spherical collapse model in degenerate higher-order scalar-tensor (DHOST) theories beyond Horndeski, employing the effective field theory (EFT) of dark energy approach. We…