The virial theorem in Eddington-Born-Infeld gravity

Understand

We consider the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides an alternative explanation for the mass discrepancy in clusters of galaxies.

• For this purpose we derive the modified Einstein field equations, finding an additional "geometrical mass" term which provides an effective contribution to the gravitational binding energy.
• Using some approximations and assumptions for weak gravitational fields, and taking into account the collisionless relativistic Boltzmann equation, we derive a generalized version of the virial theorem in the framework of EBI gravity.
• We show that the "geometrical mass" term may account for the well known virial mass discrepancy in clusters of galaxies.