DHOST gravity in Ultra-diffuse galaxies -- Part I: the case of NGC1052-DF2

The Ultra-Diffuse galaxy NGC1052-DF2 has recently been under intense scrutiny because from its kinematics it has revealed to be "extremely deficient" in dark matter, if not lacking it at all. This claim has raised many questions and solutions regarding the relationship between baryons and dark matter in Ultra-Diffuse galaxies. But there seems to be a quite unanimous belief that, if such very low dark matter content is confirmed and extended to other similar galactic objects, it might be a deathblow to theories which modify and extend General Relativity. Deficient dark matter galaxies thus represent a fertile ground to test both standard dark matter and modified gravity theories. In this work, we consider a specific Degenerate Higher-Order Scalar Tensor model to study the velocity dispersion of ten compact globular clusters-like objects associated with NGC1052-DF2 to infer the dynamical mass of the galaxy. Due to the partial breaking of the corresponding screening mechanism, this model can possibly have large cosmological scale effects influencing the dynamics of smaller structures like galaxies. We consider two scenarios: one in which the model only describes dark energy; and one in which it additionally entirely substitutes dark matter. We find that the best model to explain data is the one in which we have General Relativity and only stellar contribution. But while in former scenario General Relativity is still statistically (Bayesian) favoured, in the latter one the alternative model is as much successful and effective as General Relativity in matching observations. Thus, we can conclude that even objects like NGC1052-DF2 are not in contrast, and are not obstacles, to the study and the definition of a reliable alternative to General Relativity.