Preprint (12.10.2002)
Date: Sat, 12 Oct 2002 10:45:18 GMT
From:redshift0@narod.ru (Alexander Chepick)
Organization:
Newsgroups: sci.physics, sci.astro, alt.sci.physics.new-theories
Subject: decreasing of the value H₀
Key words: Hubble Constant

Why the Hubble parameter grows up?

A.M. Chepick, Nizhni Novgorod,
 e-mail: redshift0@narod.ru

Abstract
The increase during time of the Hubble parameter is explained from the point of view of the static universe model. Also it is demonstrated why measurements give now and will give in future a decreasing of the Hubble constant.

1. Introduction

In 1995 when models of the universe with decreasing rate of the scale factor's growth were still considered as the most probable, Tammann [1] has made a prediction, what by July, 1, 2007 exact value of the Hubble constant will be established: H₀=55 km/s/Mpc. This statement was based on restriction of age of the universe, and on the noticed decreasing of size of the Hubble constant from measurement to measurement. The Hubble constant behaved incorrectly, not fitting to the accepted models of the universe with zero cosmological constant.

But right at the end of XX century two independent groups of researchers headed by S. Perlmutter [2, (further P1998)] and W. Freedman [3, (further F2000)] have found out the phenomenon of the accelerated expansion of the universe.

This unexpected result is deduced as consequence of the proved increase during time of Hubble parameter what has forced scientists to recollect Einstein's idea about nonzero cosmological constant and to search for its explanation.

The specified conclusion has been made on the basis of the Big Bang theory (BB). Meanwhile, the conclusion about such behavior of Hubble parameter follows easily from model of the static universe.

2. Hubble constant in the expanding universe

In tables 6,9,10 [F2000] it is possible to see, how Hubble parameter decreases with growth of distance up to objects, what corresponds to growth of Hubble parameter during time. We shall express Hubble parameter H(t) through the scale factor a(t): H(t) = a'(t)/a(t), where t - time past from the moment of the Big Bang. The Hubble constant is value of Hubble parameter at the current moment t₀: H₀=H(t₀). Growth H(t) tells that the scale factor should increase not simply, but with acceleration. In turn, the accelerated growth of the scale factor tells about infinite expansion of the universe, without transition in a stage of compression. It brings an attention to the question before cosmology not only what was up to and during the Big Bang but also what will be after that, because representation about possible �yclicity, repeatability of existence of the universe does not satisfy any more now.

Besides, the question about the reasons generating nonzero cosmological constant has appeared. Attempt to explain its action with the help of Kazimir Effect does not satisfy, because it is completely not clear, how Kazimir force influences on metric of the the space and increases the scale factor, so as it changes the metric distance between objects, but at the same time it not shift these objects from their places. And if the objects are moving, then these forces should have such energy, that the far galaxies would move concerning us with by almost light's speed. Besides there is no proof , what the greater "volume" of vacuum will give stronger the Kazimir Effect. It is what should be carried out for prospective action of the cosmological constant.

And one more remark is about stationarity of the orbit. In particular, orbit's stationarity of the Earth is necessary for existence of life on our planet. Clearly, that speed of change a'(t) of the scale factor a(t) is nonzero as Hubble parameter is nonzero. Hence, the scale factor is variable. If expansion of Universe is the comprehensive phenomenon, then electromagnetic and gravitational forces should correspond strictly to change of the scale factor a(t)>1 for neutralization of this expansion in atoms, bodies, planetary systems and galaxies. Assume, for example, that at some moment we have stationary orbits in some planetary system, in which the scale factor a(t)=const>1 operates. In that case the aspiration to increase of orbit radius is compensated to the greater value of gravitational constant G, than in a case a(t)=1. But if the scale factor is variable then any value G cannot provide the stationarity of planet's orbit in this star system, as the variable increase in radius of an orbit results to variable decreasing of gravitational attraction force. And it would not been compensated by any constant value G. That is, the orbit of a planet have to be non-stationary. And as it isn't so, the scale factor can not act (as its operating will not be balanced) within the limits of a gravitational field, at least, there, where the attractive force is directed to one center of mass and there can be cyclical orbits (therefore we see the galaxies do not expanded).

In tables 1,2 [�1998] the redshifts and magnitudes of Supernovae Ia type at the top of their luminosity are given. These data have allowed to Perlmutter to announce about unexpected behavior of Hubble parameter depending on redshift. dependence of on. The similar data from the tables 6,7,9,10 [F2000] have confirmed this conclusion. In particular, in �1998 it has been noticed, that "Supernovae in redshift z = (0.3-1.0) give on the average on 0.28 mag the greater distance, than expected" (it was implied  Λ=0). It is equivalent to reception of energy smaller than counted, from the object which is set on known distance or redshift.

Let's consider more in detail the formula of luminosity:

E = L /(R₀² ψ²(z) K(z) A(z)),

where E - accepted power of a stream of energy, L - luminosity of object, R₀=c/H₀,  R₀ψ(z) - metric function of distance (depends on the chosen model), K(z) - �-correction, A(z) - factor of absorption.[�1998]

As energy from far object comes less than counted (for a given z) it is necessary to define, that distance R₀=c/H₀ should be longer, but for this purpose it is necessary to reduce H₀ . We received not only increasing H(t), but also decreasing of H₀.

As we, aspiring to increase accuracy of definition H₀, try to increase data volumes for this purpose therefore it is necessary to take more and more far objects (in course of time opportunities of astronomers grow). But farther objects give smaller value H₀ , it affects on an average results of measurements. Hence, this process of "decreasing of constant H₀" will proceed until models of the Big Bang with  Λ=0 is used.

3. Hubble constant in the Static Universe

The formula of dependence of distance R_S from redshift z in the Static Universe has form:

R_S(z) =c/H₀ ln(z+1)

The conclusion of this formula is given by many authors: Zwicky (1929) [4], Hubble (1932), Veinik (1969), LaViolette (1986) [5], Zhuck N.A. (1989) [6], etc., in their articles.

Let's analyze this dependence. For z=0 the ratio is executed: R_S(0)=R_BB(0)=0. For small z the ratio is executed: R_S(z)≈R_BB(z)≈zc/H₀. In static universe distance R_S(z) is not limited. But for any model BB a distance R_BB(z) goes up to a limit: R_BB(z) <c/H₀.  Hence, R_S(z)>R_BB(z) for z> 0.

Last inequality demonstrates, why visible luminosity of objects should increase in the Static Universe in comparison with BB. Moreover, this conclusion is true for any model BB because of it is made without a concrete definition of size of the cosmological constant. Hence, the conclusion about "decreasing of constant H₀" will be true until any models BB with any   Λ is used.

Calculation of increase in distance (in magnitudes) for SNe Ia in the Static Universe in comparison with flat model BB with  Λ=0, Ω =1 under the Mattig metric formula: R_BB(z)=2(c/H₀)[1- (z+1)^-1/2], has given for z = (0.3÷1.0) increase on the average on 0.26 mag the greater distance.

4. Conclusions

1. The counted increase in magnitudes SNe Ia in the static universe in comparison with model BB with   Λ=0 , Ω =1 for z = (0.3÷1.0) has coincided with actual.

2. Supernovae in redshift z = (1.0÷1.5) will give on the average on 0.13 mag the greater distance, than expected for  Λ> 0 (on 0.43 mag the greater distance, than expected for   Λ=0).

3. The conclusion about "decreasing of constant H₀" will be true until any models BB with any   Λ is used.

References
1. Tammann G.A. " The Hubble Constant: A Discourse. " 1996PASP.. 108.1083T
2. Astro-ph/9812133 v1 8 Dec 1998 " MEASUREMENTS OF O AND ? FROM 42 HIGH-REDSHIFT SUPERNOVAE ", S. Perlmutter et all], (P1998).
3. Astro-ph/0012376 v1 18 Dec 2000. " Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant " Wendy L. Freedman et all], (F2000).
4. Zwicky, F., 1929, Proc. Nat. Ac. Sc., Washington, 15, 773.
5. LaViolette, P. A., 1986...301:544L
6. Zhuck, N.A., "Cosmology", Kharkiv: JsC "Universe Model",2000

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