We study observational constraints on a specific dark energy model in the framework of Gleyzes-Langlois-Piazza-Vernizzi theories, which extends the Galileon ghost condensate (GGC) to the domain of beyond Horndeski theories. In this model, we show that the Planck cosmic microwave background (CMB) data, combined with datasets of baryon acoustic oscillations, supernovae type Ia, and redshift-space distortions, give the tight upper bound |αH(0)|≤O(10-6) on today's beyond-Horndeski (BH) parameter αH. This is mostly attributed to the shift of CMB acoustic peaks induced by the early-time changes of cosmological background and perturbations arising from the dominance of αH in the dark energy density. In comparison to the Λ cold dark matter (ΛCDM) model, our BH model suppresses the large-scale integrated-Sachs-Wolfe tail of CMB temperature anisotropies due to the existence of cubic Galileons, and it modifies the small-scale CMB power spectrum because of the different background evolution. We find that the BH model considered fits the data better than ΛCDM according to the χ2 statistics, yet the deviance information criterion (DIC) slightly favors the latter. Given the fact that our BH model with αH=0 (i.e., the GGC model) is favored over ΛCDM even by the DIC, there are no particular signatures for the departure from Horndeski theories in current observations.
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