No no. Gravity is curvature of space-time. Not mass. The curvature has a magnitude and a direction, so it's a vector field.
Thank you sayak83, you are absolutely right, my statement was totally wrong.
Higgs field theory says that mass property of quarks and some leptons are the values that define their interactions with Higgs field, and in the early hot universe these interactions were broken, and their mass were zero. Now, since Higgs field and gravity field are two different fields, do we have a new property for these particles that define the value of their gravity field? Because, with mass = 0, there is no gravity field.
Also, in this new definition for mass, does mass still relates to the energy of the particle (E = mc^2)? Because, in the early hot universe the energy of quarks and some leptons become zero, and I think this cannot be right either.
Also, with Higgs field we are interjecting that in the early hot universe quarks and some of leptons had zero mass, and these particles were moving like photons. In thermodynamic heat is defined by motion of particles, but at this extreme density, is any motion feasible?