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The modified Hubble-relation.
Negative Expansion-acceleration of the Universe?

By Louis Nielsen   http://www.rostra.dk/louis

In the following considerations about a modified Hubble-relation where
the Hubble-function H(T) is determined by a decreasing gravitational
'constant' according to the relation:

(1)   H(T) = - (dG/dT)*(1/G) = (1/3)*(1/T)

In equation (1) (dG/dT) is the time derivative of the variable
decreasing gravitational 'constant' G and T is the actual age of the
Universe.
The mathematical connection between H(T) and T gives a hyperbola
curve.

The modified Hubble-relation is given by:

(2)   v(T) = H(T)*D(T)

In equation (2) v(T) is the radial velocity of for example a galaxy at
the time T and D(T) is the distance to the galaxy at the time T.

By differentiation of the velocity in equation (2) we get the
acceleration a(T) of the galaxy at the time T when it is in a distance
D(T). We get:

(3)   a(T) = (- 2/9)* (D(T)/T^2)

>From equation (3) we see that the acceleration a is negative! The
velocity of the galaxy is decreasing.

We can rewrite equation (3) so we have a relationship between a(T),
v(T) and T. We get:

(4)   a(T) = (-2/3)* (v(T)/T)

>From equation (4) we see: The negative acceleration of a given galaxy
is inversely proportional to the actual age T of the Universe and
directly proportional to the velocity v(T)

Examples:
If T = 15*10^9 years = 4.7*10^17 sec and v(T) = 3*10^5 m/s then we get
an enormous small negative value for the acceleration given by:

(5)   a(T) = - 4.3*10^(-13) m/s^2

If  T = 1*10^9 years = 3.15*10^16 sec and v(T) = 1*10^7 m/s we get:

(6)   a(T) = - 2.1*10^(-10) m/s^2

Conclusion of the above considerations:
We see that the cosmic accelerations of the galaxies are negative and
that the values are enormous small.
If the above considerations are right then the Universe is
acceleration in its expansion but with a negative acceleration which
over time will brake up the expansion.

My question to all of you:
Is it ultimately found that the Universe is in an accelerated
expansion and is it ultimately found that the acceleration is positive
or can it be that the acceleration is negative? And what are the
measured (calculated) values of the expansion-acceleration?

PS: Is the observed acceleration-anomaly of the Pioneer Probes
explained by the above considerations?

Best regards
Louis Nielsen
Denmark
http://www.rostra.dk/louis