repulsive dark matter Repulsive dark matter (p3)
...If we assume the thermal velocities, in both folds, to be negligible with respect to the velocity of light, the pressures can be neglected (zero-pressure dust universes model). In a first step, when decoupling has just occurred, we assume r = r* and the system becomes :
(12-a)
(12-b)
(12-c)
(12-d)
...From (12-b) and (12-d) the curvature indices k and k* must be negative. The evolution laws are simply linear : R = R* » t
...After that short period (the very beginning of the matter dominated era), we return to the system (11-a) to (11-d), with curvature indices k = k* = -1 :
(13-a)
(13-b)
(13-c)
(13-d)
from which we get immediately :
(14-a)
(14-b)
Introducing the mass-conservation in both folds :
(15) r R³ = r* R*³ = ro Ro³ = constant
ro and Ro being characteristic quantities. Let :
(16)
(17)
Then the system becomes :
(18-a)
(18-b)
...Notice that R = R* gives R" = R*" = 0. On the other hand, if the two universes were "fully coupled", i.e. R*/R = constant, then they would correspond to Friedmann models, with "parallel evolutions". But we consider that they are coupled by the gravitational field, through (18-a) and (18-b), which show that the linear expansion is unstable. If, for example R > R* then R" > 0 and R*" < 0 . The system can be solved numerically. The typical solution corresponds to figure 5.
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Fig. 5 : The evolution of the scale parameters of the universe and dark universe.
...With respect to the classical Friedmann model, this new model enlarges the age of the universe. It depends on the retained value of the Hubble constant Ho. In 1993 measurements from Hubble telescope increased the constant from 45 to 70 km/s/Mpc, which, based on the Einstein de Sitter model with zero cosmological constant, gave an age of the universe lying between 8 and 9 billion years, and raised a serious problem with respect to the age of the oldest stars of our galaxy. But more recent calibration of cepheids, from Hipparcos satellite measurements, lowered Ho. At the same time some people tended to lower the estimated age of the oldest stars of our galaxy.
...Notice that the repulsive dark matter plays the role of a "cosmological constant", for it gives a positive acceleration R" in our fold.
Anyway, the discussion about the age of the universe is not ended.
