We study "classical" bouncing and Genesis models in beyond Horndeski theory. We give an example of spatially flat bouncing solution that is non-singular and stable throughout the whole evolution. We also provide an example of stable geodesically complete Genesis with similar features. The model is arranged in such a way that the scalar field driving the cosmological evolution initially behaves like full-fledged beyond Horndeski, whereas at late times it becomes a massless scalar field minimally coupled to gravity.
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A 2017 study studied this question.