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f (R) gravity is one of the simplest viable modifications to General Relativity: it passes local astrophysical tests, predicts both the early-time cosmic inflation and the late-time cosmic acceleration, and describes dark matter. In this paper, we probe cosmic magnification on large scales in f (R) gravity, using the well-known Hu-Sawicki model as an example. Our results indicate that at redshifts |$z \, {\lt }\, 3$|⁠ , values of the model exponent |$n \, {\gt }\, 1$| lead to inconsistent behaviour in the evolution of the scalar perturbations. Moreover, when relativistic effects are taken into account in the large-scale analysis, our results show that as z increases, large-scale changes in the cosmic magnification angular power spectrum owing to integral values of n tend to share a similar pattern, while those of decimal values tend to share another. This feature could be searched for in the experimental data, as a potential 'smoking gun' for the given class of gravity models. Furthermore, we found that at |$z \, {=}\, 1$| and lower, relativistic effects lead to a suppression of the cosmic magnification on large scales in f (R) gravity, relative to the concordance model; whereas, at |$z \, {\gt }\, 1$|⁠ , relativistic effects lead to a relative boost of the cosmic magnification. In general, relativistic effects enhance the potential of the cosmic magnification as a cosmological probe. [ABSTRACT FROM AUTHOR]

In the context of f ( R ) gravity theories, we show that the apparent mass of a neutron star as seen from an observer at infinity is numerically calculable but requires careful matching, first at the star’s edge, between interior and exterior solutions, none of them being totally Schwarzschild-like but presenting instead small oscillations of the curvature scalar R ; and second at large radii, where the Newtonian potential is used to identify the mass of the neutron star. We find that for the same equation of state, this mass definition is always larger than its general relativistic counterpart. We exemplify this with quadratic R 2 and Hu–Sawicki-like modifications of the standard General Relativity action. Therefore, the finding of two-solar mass neutron stars basically imposes no constraint on stable f ( R ) theories. However, star radii are in general smaller than in General Relativity, which can give an observational handle on such classes of models at the astrophysical level. Both larger masses and smaller matter radii are due to much of the apparent effective energy residing in the outer metric for scalar–tensor theories. Finally, because the f ( R ) neutron star masses can be much larger than General Relativity counterparts, the total energy available for radiating gravitational waves could be of order several solar masses, and thus a merger of these stars constitutes an interesting wave source. [ABSTRACT FROM AUTHOR]