In GR calculations below the cosmological scale, it is conventional to assume that a sufficient distance from the central object, space becomes flat. However, when that object is a galaxy or similar, it seems to me that it might be better to assume that the boundary is more like the 3-D equivalent of a cone, constituting a fraction (m/M) of the total solid angle needed to close the universe, where m is the local mass and M is the mass of the universe. If one assumes that the area of an enclosing sphere has been decreased by a factor (1-m/M), then linear dimensions have been decreased by approximately the square root of that, (1-m/2M). That forms the cosine of the angle by which the "conical" space diverges from being flat, so the sine and hence the angle relative to flat space is approximately sqrt(m/M). The curvature of the "cone" is 1/r times this, and it seems plausible that for slow-moving objects this could give rise to an additional acceleration relative to flat space of c^2/r sqrt(m/M). Note that this formula was only reached by somewhat imprecise analogies, so the above is not actually a rigorous derivation, and even if the analogies are valid it could still hide factors of 2 or similar. However, the resulting formula seems quite promising. In MOND, when the acceleration due to normal gravity becomes low enough, a different term in the acceleration comes into effect which is of the form sqrt(G m a_0)/r. This matches the above formula if the MOND acceleration parameter a_0 is equal to c^4/GM. The experimental value of a_0 is around 1.2*10^-10 ms^-2 so this matches the formula if the mass of the universe is approximately 10^54 kilograms. This is certainly around the right order of magnitude, which seems very interesting, given that this formula was derived from an idea relating to the shape of space and the closure of the universe, unlike MOND itself which is (as far as I know) purely empirical at present. In this case, the extra acceleration would merely be added to the Newtonian acceleration, which in the MOND formalism is formally equivalent to using an interpolation function of the following form, assuming my calculations were correct: mu(x) = (sqrt(1+1/4x)-sqrt(1/4x))^2 (I found it quite surprising that the above expression is equal to x when x is small, as I would not have guessed that at first glance). Does anyone know whether this interpolation function (based on adding the accelerations together) is considered viable with current galaxy data? This formula c^2/r sqrt(m/M) has another curious feature, which is however far from cosmological. I found this when I was investigating under what conditions the MOND and Newtonian accelerations are comparable. Specifically, consider the acceleration at the surface of a particle of mass m and Compton radius r = hbar/mc, and consider when it is equal to the "conical space" acceleration: Gm/r^2 = c^2/r sqrt(m/M) Moving some factors of c and r around we get Gm/rc^2 = sqrt(m/M) If we substitute the Compton radius expression for r, we get: Gm^2/(hbar c) = sqrt(m/M) Squaring and rearranging this, we get m^3 = ((hbar c/G)^2)/M or m = cube root of (((hbar c/G)^2)/M) If we use M = 10^54 kg from matching the MOND result, this gives m = approx 34 MeV/c^2 That is, the mass for which these two acceleration expressions are equal is around 65 times the mass of the electron, around the right order of magnitude for all common particles. No, I don't know whether either of the above results (MOND or particle) is physically meaningful, but I just thought they both seemed rather interesting.