Cosmological models with Galileon gravity are an alternative to the standard ACDM 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-l(Tg), of CMB temperature maps and foreground galaxies from the WISE survey. The sign of C-l(Tg) 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 ACDM), 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-l(Tg) and exhibits a 7.8 sigma 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 ACDM. The data prefers a non zero sum of the neutrino masses (Sigma m(v) approximate to 0.5eV) with similar to 5 sigma significance in these models. The best-fitting models have values of Ho consistent with local determinations, thereby avoiding the tension that exists in ACDM. We also identify and discuss a similar to 2 sigma 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.

The existence of cosmic superstrings may be probed by astronomical time domain surveys. When crossing the line of sight to point-like sources, strings produce a distinctivemicrolensing signature. We consider two avenues to hunt for a relic population of superstring loops: frequent monitoring of (1) stars in Andromeda, lensed by loops in the haloes of the Milky-Way and Andromeda and (2) supernovae at cosmological distances, lensed by loops in the intergalactic medium. We assess the potential of such experiments to detect and/or constrain strings with a range of tensions, 10(-15) less than or similar to G mu/c(2) less than or similar to 10(-6). The practical sensitivity is tied to cadence of observations which we explore in detail. We forecast that high-cadence monitoring of similar to 10(5) stars on the far side of Andromeda over a year-long period will detect microlensing events if G mu/c(2) similar to 10(-13), while similar to 10(6) stars will detect events if 10(-13.5) < G mu/c(2) < 10(-11.5); the upper and lower bounds of the accessible tension range continue to expand as the number of stars rises. We also analyse the ability to reject models in the absence of fluctuations. While challenging, these studies are within reach of forthcoming time-domain surveys. Supernova observations can hypothetically constrain models with 10(-12) < G mu/c(2) < 10(-6) without any optimization of the survey cadence. However, the event rate forecast suggests it will be difficult to reject models of interest. As a demonstration, we use observations from the Pantheon Type Ia supernova cosmology data set to place modest constraints on the number density of cosmic superstrings in a poorly tested region of the parameter space.