  Our motivation in this work is due to the great importance of relativistic
boson stars as fierce competitors of black holes which from theoretical
perspective they described by some KG complex scalar waves interacting with
curved background in general form. To do so we use the Einstein-Klein Gordon
(KG) scalar tensor gravity in presence of Coleman-Weinberg (CW)
self-interaction potential to study possible of formation of a spherically
symmetric boson star and situation of its stability. As we know the CW
potential plays an important role in description of cosmic inflation and so we
encourage to check its effects in formation of a relativistic boson star.
