Spherical Collapse in Modified Gravity Theories
  We study the spherical collapse in the Parametrized Post-Friedmannian (PPF)
scheme. We use a general form of the PPF parameter related to the Poisson
equation and found the equations to solve that includes a non-trivial fifth
force coming from the convolution of the modified gravity term in the k-space.
In order to compute a concrete model, we use the parametrization proposed by
Bertschinger and Zukin. The equations of the spherical collapse are solved
assuming a Gaussian density profile and we show there is no shell crossing
before reaching the turn around point. We show that the fifth force does not
satisfy the Birkhoff's theorem and introduces different behaviors for the
density threshold $\delta_{c}$, which in this case depends on the size and
shape of the initial density profile, and therefore one expects a different
statistic of the collapsed objects in the universe.
