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With V ~ r 3 and dV ~ r 2 dr we finally receive:
                        (41)
If we assume the universe to span out an Euclidean ( plane) space and to be homogenous and isotropic over large space, then, because of R ~ r and M ~ m, for the total universe, reslts:
                    (42)
As we could expect, this result - it demands a plane space filled with a "virtual" medium- is in agreement with eq. (7), which has been deduced from the field equations of the GTR. This "virtual" medium also could be called modern space aether which, contrary to the relativistic aether, is compatible with the STR.

Annex IV   (also see [14])

From the law of energy preservationE = M(t) c 2 (t) = const.      (43)
     we receive by differentiation:
                                                   (44)
 In this, the gradient  = dM / dt  is positive, because the „material energy“ increases with progressing time
(eq. 9).
The energy amount necessary for this  is set free by the light speed, decreasing with time  . Which part of the total material energy M is hidden in the vacuum (= gravitational space) can be quantified by a simple deliberation: By means of an idealized model of the universe, in which all „matter lumps“ are homogenously distributed and fly radially outward at distance- proportional speed, without interfering with each other, the time gradient   for the gravitationally bound space energy can be defined ( Fig. 18). For a ball sphere with radius r and wall thickness ds, the energy subtracted from the matter contained in the ball sphere, by delayed expansion during the time dt, amounts to
d(dEv) = F ds                                                                         (45)
 This is exactly the amount of energy needed to enlarge the gravitational space.

Fig. 18: Variation of space energy in time
 
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