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We present an analytical model for the evolution of brown dwarfs in quadraticPalatini f(R) gravity. We improve previous studies by adopting a more realisticdescription of the partially-degenerate state that characterizes brown dwarfs.Furthermore, we take into account the hydrogen metallic-molecular phasetransition between the interior of the brown dwarf and its photosphere. Forsuch improved model, we revise the cooling process of sub-stellar objects.

Cooling process of brown dwarfs in Palatini f(R) gravity