Scalarized black holes in
\nscalar Gauss-Bonnet models
\nwith a positive cosmological
\nconstant

Since the start of modern Astrophysics and Cosmology, two mysteries have been puzzling researchers: dark energy and dark matter. In order to tackle this, researchers have been trying to get clearer answers through the study alternative gravity models, considering higher curvature terms and/or bosonic scalar fields. The theories of modified gravity that include extra scalar fields, so-called scalar-tensor theories, present some interesting phenomenology. An intriguing possibility occurs when the additional scalar field is non-minimally coupled to the gravitational sector. The interaction between a scalar field and the strong spacetime curvature of a black hole originates what is known as scalarization. The latter endows BHs surrounded by a real scalar field with interesting and distinct characteristics. Alternatively, low-compactness objects that do not have enough curvature can be helped by the presence of a positive cosmological constant, allowing objects like
\ngalaxies and galaxy clusters to suffer scalarization, adding an extra mass profile outside
\nof the observable matter. It then follows the possibility for this matter profile to
\nmimic the observed dark matter. For this study, we will consider scalarized objects in an
\nextended scalar-tensor theory where the scalar field is non-minimal coupled through a
\nquartic coupling function to the Gauss-Bonnet invariant and in the presence of a positive
\ncosmological constant. Firstly, the equations of motion for the metric and the scalar field
\nwere obtained from the action. Then, through the numerical method Runge-Kutta with
\na shooting method, the profiles of the scalar field between the Schwarzschild horizon and
\nthe cosmological horizon were derived for various values of the coupling constant β and
\nΛ. Finally, plots of β related to the main parameters of the problem have been extracted
\nfrom the results of the integration and the plots of BH evolutionary branches.