Cosmological models with Galileon gravity are an alternative to the standard { \Lambda { CDM } } 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 _ { \ell } ^ { Tg } , of CMB temperature maps and foreground galaxies from the WISE survey .
The sign of C _ { \ell } ^ { 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 { \Lambda { CDM } } ) , 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 _ { \ell } ^ { 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 { \Lambda { CDM } } .
The data prefers a non zero sum of the neutrino masses ( \sum m _ { \nu } \approx 0.5 eV ) with \sim 5 \sigma significance in these models .
The best-fitting models have values of H _ { 0 } consistent with local determinations , thereby avoiding the tension that exists in { \Lambda { CDM } } .
We also identify and discuss a \sim 2 \sigma tension that Galileon gravity exhibits with recent BAO measurements .
Our analysis shows overall that Galileon cosmologies can not be ruled out by current data but future lensing , BAO and ISW data hold strong potential to do so .