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Cosmological models with Galileon gravity are an alternative to the standard ΛCDM paradigm with testable predictions at the level of its self-accelerating solutions for the expansion history, as well as large-scale structure formation. Here, we place constraints on the full parameter space of these models using data from the cosmic microwave background (CMB) (including lensing), baryonic acoustic oscillations (BAO) and the Integrated Sachs-Wolfe (ISW) effect. We pay special attention to the ISW effect for which we use the cross-spectra, C ℓTg , of CMB temperature maps and foreground galaxies from the WISE survey. The sign of C ℓTg is set by the time evolution of the lensing potential in the redshift range of the galaxy sample: it is positive if the potential decays (like in ΛCDM), negative if it deepens. We constrain three subsets of Galileon gravity separately known as the Cubic, Quartic and Quintic Galileons. The cubic Galileon model predicts a negative C ℓTg and exhibits a 7.8σ tension with the data, which effectively rules it out. For the quartic and quintic models the ISW data also rule out a significant portion of the parameter space but permit regions where the goodness-of-fit is comparable to ΛCDM. The data prefers a non zero sum of the neutrino masses (∑m ν 0.5eV) with ∼ 5σ significance in these models. The best-fitting models have values of H 0 consistent with local determinations, thereby avoiding the tension that exists in ΛCDM. We also identify and discuss a ∼ 2σ tension that Galileon gravity exhibits with recent BAO measurements. Our analysis shows overall that Galileon cosmologies cannot be ruled out by current data but future lensing, BAO and ISW data hold strong potential to do so.

We present high signal-to-noise galaxy-galaxy lensing measurements of the Baryon Oscillation Spectroscopic Survey constant mass (CMASS) sample using 250 deg2 of weak-lensing data from Canada-France-Hawaii Telescope Lensing Survey and Canada-France-Hawaii Telescope Stripe 82 Survey. We compare this signal with predictions from mock catalogues trained to match observables including the stellar mass function and the projected and twodimensional 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 per cent larger than observed. Detailed tests show that our results are robust to a variety of systematic effects. Lowering the value of S8 = σ8 √ Ωm/0.3 compared to Planck Collaboration XIII 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 ΔΣ 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 effect 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.