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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 $δ_{c}$, 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.