I'm trying to derive Friedmann's equation for cosmology using Newtonian physics. I've got the force equation F=ma for the case without a cosmological constant. But now I'm trying to incorporate the cosmological constant into this force equation. But I'm having trouble seeing how the cosmological constant can appear to apply a force on some particle at the edge of a spherical universe of radius R. I thought that I might get somewhere through dimensional analysis if I could understant the units of the cosmological constant from its use in the Einstein Field Equation where it was initially introduced. But I find I don't know the units of any of the other entities in the EFE - the units for the metric gab or the Ricci tensor or the Ricci scalar or the energy-momentum tensor. Do the units change for different values of ab? It seems everyone likes using elaborate mathematics - and I don't see much practical use - not even dimensional units of the things they talk about. Any help out there? Thanks.