Observations show that the current density of the Universe is close to the critical density:(adsbygoogle = window.adsbygoogle || []).push({});

rho = 3 H_0^2 / 8 Pi G

Assuming a spherical observable Universe of constant density, together with the relation c = H_0 * R, one can rearrange the above equation to give the relation:

G * M / R = c^2 / 2

where M is the mass and R is the radius of the observable universe at the current cosmological time.

Perhaps this is a fundamental relationship that holds at all times. It seems to embody Mach's principle in that it says that half the mass/energy of any particle comes from the mutual gravitational potential energy between the particle and the rest of the observable Universe. (To see this multiply both sides by the particle mass m). In fact this relationship seems to provide a natural definition of the "observable" universe as the "gravitationally interacting" Universe.

If you plug the above relationship into the Friedmann equations one gets a linearly expanding model that behaves exactly like the massless Milne model!

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# Critical density formula hides fundamental relationship?

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