We investigate the turnaround radius in the spherical collapse model, both in General Relativity and in modified gravity, in particular f (R) scenarios. The phases of spherical collapse are marked by the density contrast in the instant of turnaround δ t , and by the linear density contrast in the moment of collapse, δ c . We find that the effective mass of the extra scalar degree of freedom which arises in modified gravity models has an impact on δ t of up to ∼ 10%, and that δ c can increase by ∼ 1.0%. We also compute the turnaround radius, R t , which in modified gravity models can increase by up to ∼ 6% at z 0.

We investigate the relationship between the turnaround radius R t and the virial mass M v of cosmic structures in the context of ΛCDM model and in an f (R) model of modified gravity -namely, the Hu-Sawicki model. The turnaround radius is the distance from the center of the cosmic structure to the shell that is detaching from the Hubble flow at a given time, while the virial mass is defined, for this work, as the mass enclosed within the volume where the density is 200 times the background density. We employ a new approach by considering that, on average, gravitationally bound astrophysical systems (e.g., galaxies, groups and clusters of galaxies) follow, in their innermost region, a Navarro-Frenk-White density profile, while beyond the virial radius (R v ) the profile is well approximated by the 2-halo term of the matter correlation function. By combining these two properties together with the information drawn from solving the spherical collapse for the structures, we are able to connect two observables that can be readily measured in cosmic structures: the turnaround radius and the virial mass. In particular, we show that, in ΛCDM, the turnaround mass at z = 0 is related to the virial mass of that same structure by M t 3.07 M v , while in terms of the radii we have that R t 3.7 R v (for virial masses of 10 13 h −1 M ). In the f (R) model, on the other hand, we have M t 3.43 M v and R t 4.1 R v , for |f R0 | = 10 −6 and the same mass scale. Therefore, the difference between ΛCDM and f (R) in terms of these observable relations is of order ∼ 10−20% even for a relatively mild strength of the modification of gravity (|f R0 | = 10 −6 ). For the turnaround radius itself we find a difference of ∼ 9% between the weakly modification in gravity considered in this work (|f R0 | = 10 −6 ) and ΛCDM for a mass of 10 13 h −1 M . Once observations allow precisions of this order or better in measurements of the turnaround R t , as well as the virial mass M v (and/or the virial radius R v ), these quantities will become powerful tests of modified gravity.

The influence of Lorentz- and CPT-violating terms of the extended Standard Model on a semi-classical two-level system is analyzed. It is shown that the Lorentz-violating background (when coupled with the fermion sector in a vector way) is able to induce modifications on the Rabi oscillation pattern, promoting sensitive modulations on the usual oscillations. As for the term involving the coefficient coupled in an axial vector way, it brings about oscillations both on energy states and on the spin states (implied by the background). It is also seen that such backgrounds are able to yield state oscillations even in the absence of the electromagnetic field. The foreseen effects are used to establish upper bounds on the Lorentz-violating coefficients.Comment: 13 pages, 6 figures, revtex style