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Original
2015
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Then

J. Ben Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui and G. Tasinato, “Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order,” JHEP 1612
Original
2016
Later among the works it cites.
R. K. Jain, C. Kouvaris and N. G. Nielsen, “White Dwarf Critical Tests for Modified Gravity,” Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
E. Babichev, K. Koyama, D. Langlois, R. Saito and J. Sakstein, “Relativistic Stars in Beyond Horndeski Theories,” Class. Quant. Grav. 33
Original
2016
Later among the works it cites.
J. Sakstein, H. Wilcox, D. Bacon, K. Koyama and R. C. Nichol, “Testing Gravity Using Galaxy Clusters: New Constraints on Beyond Horndeski Theories,” JCAP 1607
Original
2016
Later among the works it cites.

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2018

Matter bispectrum beyond Horndeski

Hirano, Shin'ichi, Kobayashi, Tsutomu, Tashiro, Hiroyuki et al.

Understand

The Horndeski scalar-tensor theory and its recent extensions allow nonlinear derivative interactions of the scalar degree of freedom.

We study the matter bispectrum of large scale structure as a probe of these modified gravity theories, focusing in particular on the effect of the terms that newly appear in the so-called "beyond Horndeski" theories.
We derive the second-order solution for the matter density perturbations and find that the interactions beyond Horndeski lead to a new time-dependent coefficient in the second-order kernel which differs in general from the standard value of general relativity and the Horndeski theory.
This can deform the matter bispectrum at the folded triangle configurations ($k_1+k_2=k_3$), while it is never possible within the Horndeski theory.