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I think my argument is better this way round.

1/ Assume that space is flat and that there is no cosmological constant.

2/ Assume that the size of the universe R is bounded by the distance a light beam travels in the age of the Universe t.

Therefore:

R = c * t

Putting this into the Friedman equations for the evolution of the universe we find the following consequences:

1/ 2 * G * M / R = c^2

where M is the mass of the universe and R is the size of the universe.

If you multiply both sides of equation (1) by the mass of a particle m you get a statement of Mach's principle that half the mass/energy of any particle is equal to its mutual gravitational energy with every other particle in the Universe.

2/ A dark energy exists with the following formula for its mass density rho :

rho = (1 / 8 pi G) * 1 / t^2

where t is the age of the universe.

John

1/ Assume that space is flat and that there is no cosmological constant.

2/ Assume that the size of the universe R is bounded by the distance a light beam travels in the age of the Universe t.

Therefore:

R = c * t

Putting this into the Friedman equations for the evolution of the universe we find the following consequences:

1/ 2 * G * M / R = c^2

where M is the mass of the universe and R is the size of the universe.

If you multiply both sides of equation (1) by the mass of a particle m you get a statement of Mach's principle that half the mass/energy of any particle is equal to its mutual gravitational energy with every other particle in the Universe.

2/ A dark energy exists with the following formula for its mass density rho :

rho = (1 / 8 pi G) * 1 / t^2

where t is the age of the universe.

John

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