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We use the cross-correlation power spectrum of the integrated Sachs-Wolfe(ISW) effect in the cosmic microwave background (CMB) temperature anisotropyand galaxy fluctuations to probe the physics of late-time cosmic acceleration.For this purpose, we focus on three models of dark energy that belong to asub-class of Horndeski theories with the speed of gravity equivalent to that oflight: Galileon Ghost Condensate (GGC), Generalized Cubic Covariant Galileon(GCCG), and K-mouflage. In the GGC and GCCG models, the existence ofcubic-order scalar self-interactions allows a possibility for realizingnegative ISW-galaxy cross-correlations, while the K-mouflage model predicts apositive correlation similar to the $\Lambda$-cold-dark-matter (LCDM) model. Inour analysis, we fix the parameters of each model to their best-fit valuesderived from a baseline likelihood analysis with observational data from CMB,baryon acoustic oscillations, and supernovae type Ia. Then we fit thosebest-fit models to the ISW-galaxy cross-correlation power spectrum extractedfrom a collection of photometric redshift surveys. We find that both GGC andGCCG best-fit models degrade the fit to the ISW-galaxy cross-correlation datacompared to LCDM best-fit model. This is attributed to the fact that, for theirbest-fit values constrained from the baseline likelihood, the cubic-orderscalar self-interaction gives rise to suppressed ISW tails relative to$\Lambda$CDM. The K-mouflage best-fit model is largely degenerate with the LCDMbest-fit model and has a positively correlated ISW-galaxy power close to thatof LCDM.

Probing Modified Gravity with Integrated Sachs-Wolfe CMB and Galaxy Cross-correlations