Spherical collapse in ΛCDM,Chameleon and Symmetron models

Late time accelerated expansion of the universe is usually considered to be the result of dark energy, and the standard model of cosmology implements the cosmological constant as the drive of the acceleration of the universe. A possible alternative to the cosmological constant is modified gravity, and screening mechanisms are a possible way to work around the local gravity constraints on modified gravity. This work implements screening mechanisms to gravitational collapse in order to investigate a wide parameter space of two screening mechanisms, the chameleon and symmetron, by numerically solving the second Friedmann equation for spherically symmetric perturbations. In particular, the effects of the chameleon and symmetron mechanisms on the density of virialized objects have been considered. It has been confirmed that heavily screened objects have a density at virialization similar to the results from a cosmological constant. Further, it has been confirmed that with these screening mechanisms virialized and unscreened objects in general have a much lower density than with a cosmological constant. However, two exceptions from this general trend was found for very late symmetry breaking in the symmetron model. These exceptions was explained as a delay in virialization due to late, full unscreening of the objects. Additionally, both the chameleon and symmetron screening mechanisms was found to have sets of the parameters which lead to a smaller density of the virialized objects than the surrounding parameters did. In particular, these sets of the parameters lead to partial, but close to maximal, unscreening of objects. Since these parameter sets are characterized by the transition from total unscreening to partial unscreening they have been dubbed the transition regimes of the models. The existence of these regimes can provide constraints on the model parameters when compared to observations of virialized halos