You have been writing that the Planck force is the force in thePlanck units. That starts in your first post. All systems of units are equal. Selecting to use one is a matter of convenience, not physics.

The Planck force is not a force between any masses, it is a unit of force like a Newton. The Planck force is not calculated, it is derived from the other Planck units. Planck force is the derived unit of force resulting from the definition of the base Planck units for time, length, and mass.

If we did an calculation of the Newtonian gravitational force between2 units of massthen we have F = G (1 kg) (1 kg)/r^2 or F = G (1 mp) (1 mp) )/r^2, or etc. The force will be related to the unit of mass squared. The distance r is irrelevant. Put it to 1 meter, 1 light-year, a billion light-year and the force is still related to the unit of mass squared.

It is the Newtonian law of gravitation has two masses in it. These can be two equal masses but that is not needed. The Newtonian law of gravitation is not used for cosmology for many reasons. For example, there is no way for the universe to expand as observed using Newtonian gravitation. Specifically in Newtonian gravitation the cosmological constant that you want to include does not exist.

Standard cosmology has the universe filled with homogeneous and isotropic matter. That is the cosmological principle. My first thought was that the well known shell theorem suggests that the net Newtonian force at any point by the surrounding matter would be zero. Maybe it is not. However it is definitely not a force that pushes mass away to create the expanding universe we observe. The Newtonian gravity between the Milky Way and other galaxies will not push them away.

Which is what I have been telling you is wrong - you divide the masses by 2 and so ignore half the baryonic mass of the universe to get a wrong value for the Planck force unit of measurement F_{p}.

The error is better stated in your post just above that equation: "so, in cosmology we need two constant mass and egal". In cosmology there are never 2 masses. There is the total mass of the universe with a homogeneous and isotropic distribution. It is a continuous distribution. Alternately you can think of it as an infinite number of masses. The actual universe has many more than 2 masses in it, e.g. maybe 2 trillion galaxies each with billions of stars. One thing that the cosmological principle does is allow cosmology to have solutions that are relatively easy to calculate.

N.B. We do not know how big the universe is or even if it has a size and so cannot know the mass of the universe. We can estimate the mass inside the observable universe. We know that the universe is much bigger (estimates of 250 times larger to 10^23 times larger to even larger) and so the baryonic mass of the universe is much bigger than that estimate. We also know that baryonic matter is a small part of the mass of the universe (there is also dark matter) and that most of the gravitational effects in GR comes from dark energy. This is why the cosmological parameters you have referred to are densities.