Brown dwarfs in Eddington-inspired Born-Infeld and beyond Horndeski theories

We studied herein the mass and the radius of brown dwarfs predicted by beyond Horndeski (BH) and Eddington-inspired Born-Infeld (EiBI) gravity theories by numerically solving the modified non-relativistic hydrostatic equations of both theories. We used a recent compilation of brown dwarf masses and radii obtained from Ref. Bayliss et al. (Astrophys J 153:1, 2016) to constrain the free parameter of both theories. We obtain the range of the corresponding parameters with 1σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} and 5σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document} confidence by using chi-squared analysis. Furthermore, the minimum chi-squared values can be reached for the cases of κ=0.17×102m5kg-1s-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa = 0.17 \times 10^2 ~\mathrm{m}^5\,\mathrm{kg}^{-1}\,\mathrm{s}^{-2}$$\end{document} and γ=-0.1207\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma = -0.1207$$\end{document} for EiBI and BH theories, respectively. The corresponding parameter values with the minimum chi-squared values are relatively small; therefore, they cannot significantly change the brown dwarf mass limits determined from the equivalence of nuclear and photosphere luminosities for the pp (hydrogen burning) and pp+pd (deuterium burning) reactions.