Spherical collapse and virialization in $f(T)$ gravities

TL;DR

This paper investigates the non-linear growth of spherical density perturbations and structure formation in $f(T)$ gravity models, analyzing virialization and constraints on initial perturbations, with implications for cosmic structure development.

Contribution

It provides the first detailed analysis of spherical collapse and virialization in $f(T)$ gravity models, including both minimal and nonminimal coupling cases, and identifies key constraints on initial perturbations.

Findings

Constraints on initial perturbation magnitude and epoch.

Nonminimal coupling models collapse slower than minimal coupling.

Perturbations within constraints can lead to structure formation.

Abstract

Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in $f(T)$ gravities. In particular, three concrete models, which have been tested against the observation of large-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of $f(T)$ gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in the magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in $f(T)$ gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.