Testing Modified Gravity Theories by Constraining the Theories Parameter Using Radius and Mass Observations of Brown Dwarfs

Modified Gravity (MOG) theories modify Poisson equation in the Newtonian limit. This MOG is also important as test-bed to analyze whether General Relativity (GR) is consistent with observations. We investigate the mass and radius of Brown Dwarfs predicted by modified Poisson equation from Beyond Horndeski (BH) and Eddington-Inspired-Born-Infeld (EiBI) theories. Brown Dwarfs are sub-stellar objects that are difficult to be detected because of their low luminosity. One of the most important properties of brown dwarfs which recently observed by Johnson and Montet[1] are radii and masses. In this note, we derive the equation of state of the stars analytically, wherein electrons part, we use exact non-relativistic degenerate ideal Fermi gas result. We also derive modified hydrostatic stellar equation predicted by MOG theories and solve them numerically to obtain their profile and mass-radius relation for each parameter on both MOG theories. We compare our theoretical results with the ones obtained Johnson and Montet [1]. (paper)