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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 this manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free. [ABSTRACT FROM AUTHOR]

The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel f(T) gravity theories using the 1 + 3 covariant formalism. After a review of the background gravitational field equations of f(T) gravity and the introduction of the covariant perturbation variables, the usual scalar and harmonic decomposition have been performed, and the analysis of the growth of the density contrasts in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and torsion-radiation mixtures is presented for the generic f(T) gravity theory. Special applications to two classes of f(T) gravity toy models, namely f (T) = μ T 0 (T T 0 ) n and f (T) = T + μ T 0 (- T T 0 ) n , have then been made within the observationally viable regions of their respective parameter spaces, and the growth of the matter density contrast for both torsion-dust and torsion-radiation epochs of the Universe has been examined. The exact solutions of the dust perturbations, with growing amplitudes in cosmic time, are obtained for some limiting cases of n. Similarly, the long- and short-wavelength modes in the torsion-radiation case are treated, with the amplitudes either oscillating or monotonically growing with time. Overall, it is noted that f(T) models contain a richer set of observationally viable structure growth scenarios that can be tested against up-and-coming observational data and can accommodate currently known features of the large-scale structure power spectrum in the general relativistic and Λ C D M limits. [ABSTRACT FROM AUTHOR]