Dark matter density distributions and dark energy constraints on structure formation including MOND

In recent papers, it was shown explicitly that the sizes of gravitationally bound large-scale cosmic structures can be constrained from the requirement that their gravitational binding self-energy density should at least be equal to the background repulsive dark energy density (for them to be bound). Here, we extend this model to incorporate various dark matter density distributions in the galaxy which are consistent with observation. We also show that the constraints set using modified Newtonian dynamics (MOND) is again consistent with observations and the same as that in the Newtonian case, hence making it impossible to distinguish between the two as also pointed out recently. We also point out that the recent observations of baryon-dominated disk galaxies formed about ten billion years ago indicate the consistency of MOND with observations.