We present high signal-to-noise galaxy-galaxy lensing measurements of the BOSS CMASS sample using 250 square degrees of weak lensing data from CFHTLenS and CS82. We compare this signal with predictions from mock catalogs trained to match observables including the stellar mass function and the projected and two dimensional clustering of CMASS. We show that the clustering of CMASS, together with standard models of the galaxy-halo connection, robustly predicts a lensing signal that is 20-40% larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. Lowering the value of S 8 = σ 8 Ω m /0.3 compared to Planck Collaboration (2015) reconciles the lensing with clustering. However, given the scale of our measurement (r < 10 h −1 Mpc), other effects may also be at play and need to be taken into consideration. We explore the impact of baryon physics, assembly bias, massive neutrinos, and modifications to general relativity on ∆Σ and show that several of these effects may be non-negligible given the precision of our measurement. Disentangling cosmological effects from the details of the galaxy-halo connection, the effects of baryons, and massive neutrinos, is the next challenge facing joint lensing and clustering analyses. This is especially true in the context of large galaxy samples from Baryon Acoustic Oscillation surveys with precise measurements but complex selection functions.

We consider the linear growth of matter perturbations on low redshifts in some f(R) dark energy (DE) models. We discuss the definition of dark energy (DE) in these models and show the differences with scalar-tensor DE models. For the f(R) model recently proposed by Starobinsky we show that the growth parameter γ0≡γ(z = 0) takes the value γ0 ≃ 0.4 for Ωm,0 = 0.32 and γ0 ≃ 0.43 for Ωm,0 = 0.23, allowing for a clear distinction from ΛCDM. Though a scale-dependence appears in the growth of perturbations on higher redshifts, we find no dispersion for γ(z) on low redshifts up to z ∼ 0.3, γ(z) is also quasi-linear in this interval. At redshift z = 0.5, the dispersion is still small with Δγ ≃ 0.01. As for some scalar-tensor models, we find here too a large value for γ′0≡(dγ/dz)(z = 0), γ′0 ≃ −0.25 for Ωm,0 = 0.32 and γ′0 ≃ −0.18 for Ωm,0 = 0.23. These values are largely outside the range found for DE models in General Relativity (GR). This clear signature provides a powerful constraint on these models.

We study the growth of matter density perturbations δm for a number of viable f (R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the parameter m ≡ Rf,RR/f,R today is larger than the order of 10 −6 , linear perturbations relevant to the matter power spectrum evolve with a growth rate s ≡ d ln δm/d ln a (a is the scale factor) that is larger than in the ΛCDM model. We find the window in the free parameter space of our models for which spatial dispersion of the growth index γ0 ≡ γ(z = 0) (z is the redshift) appears in the range of values 0.40 γ0 0.55, as well as the region in parameter space for which there is essentially no dispersion and γ0 converges to values around 0.40 γ0 0.43. These latter values are much lower than in the ΛCDM model. We show that these unusual dispersed or converged spectra are present in most of the viable f (R) models with m(z = 0) larger than the order of 10 −6 . These properties will be essential in the quest for f (R) modified gravity models using future high-precision observations and they confirm the possibility to distinguish clearly most of these models from the ΛCDM model.