Turnaround radius in Λ CDM and dark matter cosmologies with shear and vorticity

We determine the relationship between the turnaround radius, R_t, and mass, M_t, in Λ CDM, and in dark energy scenarios, using an extended spherical collapse model taking into account the effects of shear and vorticity. We find a more general formula than that usually described in literature, showing a dependence of R_t from shear, and vorticity. The R_t-M_t relation differs from that obtained not taking into account shear, and rotation, especially at galactic scales, differing ≃30% from the result given in literature. This has effects on the constraint of the w parameter of the equation of state. We compare the R_t-M_t relationship obtained for the Λ CDM, and different dark energy models to that obtained in the f(R) modified gravity (MG) scenario. The R_t-M_t relationship in Λ CDM, and dark energy scenarios are tantamount to the prediction of the f(R) theories. Then, the R_t-M_t relationship is not a good probe to test gravity theories beyond Einstein's general relativity. Copyright © 2020 American Physical Society.