In 1998 were made some new cosmological observations which by the American magazine Science were announced as "Breakthrough of the Year" (Science, December 18, 1998), The discovery was that the Universe apparently has an accelerating expansion. Scientific American, in its January 1999 issue, calls the discovery a cosmological revolution. One of the conclusions is a.o. that the Universe will continue its expansion and not - as assumed by many cosmological models - eventually change it into a contraction. The calculations made are a.o. based on spectrum analyses and measurements of luminosity of distant supernovae of the type Ia.
References:
cfa-www.harvard.edu/cfa/oir/Research/supernova/HighZ.html
and
www-supernova.lbl.gov

The conclusions of the respective teams are that supernovae, belonging to distant galaxies, are situated at distances which are greater than what would be expected according to current cosmological models. This must mean that the galaxies in question have moved faster than expected and thereby obtained a higher acceleration than what had hitherto been believed, according to these models. To save the traditional cosmological models the teams now try to introduce 'patching' solutions, supported by new and old effects, such as 'dark energy' and the re-introduction of the 'cosmological constant' in Einstein's general field equations, etc. The discovery, that distant galaxies move with a higher speed than expected by the traditional cosmological theories, is a support to my quantum theory about the Universe, – based on quantization of distance, time interval and mass. The new observations of the expansion of the Universe can be explained by my theory.
A consequence of my 'Holistic Quantum Cosmology with Decreasing Gravity' (see this) is an accelerating Universe, caused by a non lineary decrease of the gravitational forces in the Universe. Due to a continuous – quantized – decrease of the gravitational forces, the distance between two gravitating mass systems – for example two galaxies – will increase as the Universe ages. As the relative decrease of Newton's gravitational 'constant' is not lineary, this is also not the case for the increase in distance between the two systems in question. As our knowledge about the physical conditions of objects in the Universe are mainly obtained by analysis of the light emitted by the objects, it is also necessary to take into account the gravitational conditions when this light was emitted. For instance the gravitational shift of wavelength is dependent on the strength of the gravitational field in the area from which the light is emitted.

The Hubble relation and the disagreement on the value of the Hubble constant

In the traditional and established cosmology, which is based on Einstein's general theory of relativity from 1915, it is attempted to determine the numerical value of some parameters in the equations, so that a given cosmological model approaches the observations made in the real Universe. A very important quantity in these traditional, parametrized cosmological theories is the so called Hubble constant, H. It enters as a proportionality constant in the famous Hubble relation, which gives the connection between f.i. the relative radial speeds, v_r, of two galaxies, and the distance, d, between the galaxies. The Hubble relation is given by:

(1)

The Hubble relation is named after Edwin Powell Hubble (1889-1953). He discovered in 1929, that – for the stars of most galaxies – there is a systematical shift of the wavelength of the different colors towards the red part of the spectra of the stars, viz. towards longer wavelength. Hubble discovered that the relative shift of wavelength is proportional to the distance, d, between the observer and the emitting object. This discovery was quickly interpreted as a Doppler effect (discovered 1842 by Christian Doppler (1803-1853)), caused by the relative velocity of the emitting object and the observer. That the wavelengths are shifted towards red show that the emitting objects are moving away from the observer, and this is interpreted as an expansion of the Universe. The classical Doppler equation can be written:

(2)

where and c₀ is the velocity of light, the measured wavelength in the laboratory of a specific spectral line, and the difference between the measured wavelength and the measured wavelength in the loboratory. At greater velocities (about 1% of the velocity of light) it is necessary to use the relativistic Doppler equation, given by:

(3)

By measuring the relative shift of wavelength, z, of a specific spectral line, found in the light from a star in a galaxy, you can, by using (3) or (2) together with (1), determine the distance, d, to a galaxy, on the condition that you know the value of H. There is, however, considerable disagreement on this value, which the following will show.
In my quantum cosmology I do not operate directly with the Hubble constant, but it can be identified as the relative derivative of Newton's gravitational 'constant' with respect to time.

There has been – and still is – strong disagreement on the value of the Hubble constant, H. Different researchers have obtained the following values:

H₁ = 83±13 km/s/Mpc = (2.68±0.42)·10^-18 s^-1 , (Madore. Science, vol. 255, p. 405, (1992))
H₂ = 81±8 km/s/Mpc = (2.62±0.26)·10^-18 s^-1 , (S. van den Bergh. Science, vol. 270, (1995))
H₃ = 57±4 km/s/Mpc = (1.84±0.13)·10^-18 s^-1 , (A. Sandage et al., Astrophys. J. Let. vol.460, (1996))

The most cited value for the Hubble constant is H = 80±17 km/s/Mpc.
(Gravitation and Cosmology, Proceedings of the ICGC-95 Conference held at IUCAA, Pune, India on December 13-19, 1995, 1997, Kluwer Academic Publishers, see page 242).
In the above expression, Mpc is the astronomical distance unit Megaparsec: 1 Mpc = 3.086·10¹⁹ km.

Radial velocities, calculated by means of respectively the Hubble relation and my expansion equation

In chapter (2) of my 'Holistic Quantum Cosmology with Decreasing Gravity' I derive the following cosmologically general expansion formula, valid for two mass systems, moving away from each other due to the decreasing gravity:

(4)

is equal to the relative derivative of G with respect to time and is dependent on an actual age, T, of the Universe. (· denotes the first derivative with respect to time). v_r is the instantanouos value of the radial velocity of a light emitting object, relative to an observer, when light was emitted from that object, and corresponding to a retarded age of the Universe, T₁, which is lower than the actual age of the Universe.   d is the distance which the light travels in the time interval from it was emitted and until it is received – for instance by us as observers.
We note that G does not decrease linearily with the age of the Universe. The relative decrease of G was faster when the Universe was younger. When the Universe was 'born', during the first cosmical quantum time intervals, G decreased extremely fast, corresponding to what the standard theory is calling an 'inflation phase'. In our epoch G decreases very slowly, so slow that it has not hitherto been possible to measure. An exact determination of could give a simple determination of the age of the Universe. I have in my cosmology assumed that in our epoch we have (G'/G)_T ~= - 10^-18 s^-1, which gives a present actual age of the Universe of about T = 10.6·10⁹ years.
Let us calculate the radial velocity of an object from which light has been travelling 7 billion years before hitting our measuring instrument. This corresponds to a travelled distance of 7 billion light years. We thus observe and analyze light from the time when the age of the Universe was T₁ = 10.6·10⁹ years – 7·10⁹ years = 3.6·10⁹ years.
We want to calculate the radial velocity by means of respectively the Hubble relation and my expansion equation.
In order to be able to use the Hubble relation (1) we choose the following value for the Hubble constant: H = 80 km/s/Mpc.
From the Hubble relation we calculate a radial velocity:

(5)

In order to be able to calculate the radial velocity according to my equation (4) we first need to calculate the value of , when the Universe was T₁ years old. We get:

(6)

We can now calculate the radial velocity by means of my expansion formula (4). We get:

(7)

The relative procentual difference between the values in (5) and (7) is about 14%, viz. my calculated value is about 14% higher than what would be expected by using the Hubble relation. If H₁ is used in the Hubble relation, you get a relative procentual difference of about 10%, and if H₂ is used, then about 12%.

Conclusion
The radial velocity of an object , 7 billion light years distant, calculated according to my theory, is about 15% higher than what would be expected theoretically according to traditional cosmology. Thus there is good agreement with this theory and recent observations! These observations are supporting my quantum cosmology, which as one of its consequences predicts that the gravitational forces in the Universe are quantum decreasing.

Louis Nielsen, January 1999
E-mail: LNi@Herlufsholm.dk

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