a) The redshifts : Recession of the galaxies - Law of Hubble b) The expansion of the universe - General relativity - Cosmological principle c) The theory of inflation d) Cosmic Microwave Background Radiation e) Primordial nucleosynthesis f) The age of the universe g) Great structures of the universe

In fact, the constant of Hubble is rather a parameter because its value can be variable.

At the relativistic speeds, the relativistic relation of the radial Doppler effect is given by the formula:

Apart from the close universe, the redshifts are dominated by the cosmological expansion. In the Friedmann-Lemaître model, the mathematical description of the cosmological expansion, the distances are defined in the terms of metric of Robertson-Walker which is the most general mathematical description for a uniform and homogeneous space in contraction or expansion.

1) The expansion of the universe and the recession of the galaxies are not data one can observe. They rise from an interpretation of the redshifts of the remote galaxies. Other interpretations were proposed: gravitational effects, Wolf effect between 2 separated sources, gas matter in space Marmet model (1989), Symmetric Theory (1997), theory of the variable masses (Halton Arp 1999), universe of plasma (Hannès Alfvén 1989), etc... These various interpretations were not retained by the community of the researchers. The model of the author, the temporalist model, founded on the quantum constant To, proposes, in the second part of this research, a new interpretation of the redshifts and an alternative to the model of Hot Big Bang.

2) Why does the expansion of the universe start beyond the Milky Way and not below?

3) The most recent statistics on the value of Ho give for this one a value ranging between 66 and 82 Km/sec/Mpc (G.F.R. Ellis) and 47 Km/sec/Mpc (Allan Sandage). The most probable value would account for 72 Km/sec/Mpc (CMAP 2001). The corresponding value established by the author in 1962 is 67,71 Km/sec/Mpc. . The last data given by WMAP ( February 2003) made it possible to fix the value of the constant Ho of Hubble at 71 Km/sec/Mpc ( with a margin of error of 5 % ) what well confirms the temporalist value of Ho is 67,71 Km/sec/Mpc. ( http://map.gsfc.nasa.gov/m_mm/mr_limits.html ).

The standard model of Hot Big Bang comes from the equations of general relativity and of cosmological principle of a homogeneous and isotrope universe. The best measurements of expanding universe are, today, the distance from variable Cepheid stars, the relation Tully-Fisher between the disk speed of a spiral galaxy and its luminosity and the supernova of type 1a (MAP 2001).

The density of the universe determines its geometrical form and its destiny. To obtain a stable universe, Einstein proposed a cosmological constant or a density of energy of the void. When Hubble showed that the universe was expanding, Einstein rejected his cosmological constant, affirming that it constituted the most serious error of his life.

Currently, it is considered that the expansion slowed down after the Big Bang then it accelerated again. We will see in the next chapter that the cosmological constant is necessary to the inflation model created to answer the problems arising from the model of Hot Big Bang.

1) According to the cosmological principle, the universe is homogeneous and isotropic. However, the universe seems uniform only on a large scale, beyond distances from 100 to 200 Mpc. Why so?

2) The problem of the horizon: Why are the too distant areas of the universe, because they have been in contact by signals travelling at the speed of the light, almost exactly at the same temperature? The standard model of Hot Big Bang cannot answer it.

3) The observations indicate that the universe is almost entirely flat. The model of Hot Big Bang does not provide any justification for this flatness.

4) The problem of the magnetic monopolies: the model of Hot Big Bang implies, for the creation of the cores in the primordial universe, the use of the model of the Theory of Great Unification (GUTs) and the production of massive particles, the magnetic monopolies. There should remain many of them today. None was ever found up to now. Where are the magnetic monopolies?

5) The universe is born of a singularity of space-time, by the primordial explosion, with an infinite density and temperature. What is the cause of this explosion? Where do space, time and energy come from ?

To solve a certain number of problems arising from the model of Hot Big Bang, the theorists built the theory of inflation which knew various versions.

The theory of inflation worked out by Alexei Starobinsky was developed by Allan H. Guth and Paul Steinhardt (1984 - 1998), Andy Albrecht, Andrei Linde (1994 - 2001).

According to the theory of inflation, the visible universe result from a very small area of the homogeneous universe which swelled 10-35 seconds after the Big Bang. This inflationary phase lasted 10-32 seconds during which the expansion of the universe was of a factor about 10^50 then the Big Bang continued its evolution. The explosion would be a consequence of the density of energy of the void which would cause a repulsive gravity due to the existence of the cosmological constant (rejected by Einstein).

The theory of inflation would have the merit to solve a certain number of problems arising from the model of Hot Big Bang:

1) The extraordinary inflation of the universe, at speeds which are quite higher than the speed of the light, starting from a negligible and homogeneous area of the universe solves the problem of the horizon.

2) The platitude of the universe with a density close to the critical density rises from the inflation model.

3) The current absence of the magnetic monopolies is explained by the fast dispersion of those ones during the inflationary phase.

4) The inflation model envisages weak fluctuations of the Cosmic Microwave Background Radiation at the origin of the formation of the galaxies.

1) The inflation theory is a prolongation of the model of Hot Big Bang but it is independent of it.

2) The inflation theory, created to solve the problems of Hot Big Bang does not rest on any experimental fact. Its considerable extrapolation of the laws of physics does not have any theoretical justification. It only answers arbitrarily to the difficulties of the model of Hot Big Bang. It is, ultimately, only an ad hoc assumption. The assertions of the inflation theory, poorly justified, can involve a true scepticism in the eyes of rigorous observers (Peebles 2001). Moreover, the establishment of assumptions, without any observational base, leads to highly speculative and particularly contestable inflationary versions: chaotic inflation, auto-reproduction of universe, multiple universes, creations of universe in laboratory, creation of universe by a pirate physicist (physicist-hacker) and other extravagances, at light-years of the necessary scientific rigour!

3) The very weak fluctuations of the Cosmic Microwave Background Radiation cannot answer in a satisfactory way to the formation of the great structures of the universe (galaxies, clusters and superclusters, large walls, voids, etc...).

4) The existence of the cosmological constant, rejected by Einstein, necessary to the inflation model, remains, at the present time, a pure assumption, like all the assertions of the inflation model.

5) The cause of inflation, which started when 3 of the 4 fundamental interactions dissociated, remains unknown.

In 1965, Arno Penzias and Robert Wilson discovered the Cosmic Microwave Background Radiation, i.e. the microwaves radiation which fills uniformly the universe. This Cosmic Microwave Background Radiation is a radiation of blackbody at the temperature of 2,728 Kelvin degrees.

The existence of the cosmic radiation would have been envisaged, like a consequence of the model of Hot Big Bang, by Gamow.

The observation of the Cosmic Microwave Background Radiation was undertaken from 1992 by satellite COBE (Cosmic Background Explorer) then by throws of balloons (Boomerang, Maxima - 1998,1999,2000; TopHat 2001). Satellite MAP (Microwave Anisotropy Probe) launched in June 2001, then Planck programmed for 2007 must make it possible to refine measurements of the fluctuations of the fossil radiation. From various researches, it gets clear that :

1) the Cosmic Microwave Background Radiation would go back to 300.000 years after Hot Big Bang

2) a dipolar anisotropy of the radiation, by Doppler effect, due to the earthrevolving exists

3) the tiny fluctuations of the radiation with temperatures going from 2,7280 K to 2,7281 K are present

4) the search of the origin of the fluctuations of the Cosmic Microwave Background Radiation: either the inflationary phase, or the topological defects (with the possibility of cosmic strings) exist

5) the probable composition of the universe is : 5 % of baryon matter, 30 % of dark matter, 65 % of dark energy accelerating the expansion (cosmological constant? quintessence?)

Satellite MAP should bring precise details on:

1) the values of the cosmological parameters of Hot Big Bang

2) how are the structures of the galaxies in the universe formed

3) when the first structures of the galaxies were formed

4) the determination, by the study of the polarizations of the radiation, of its origin either inflationary, or topological (with the influence of the gravitational waves)

1) the Cosmic Microwave Background Radiation is not a consequence of the sole model of Hot Big Bang. Its prediction had been made, without the use of the model of Hot Big Bang, and before Gamow by: Guillaume (1896), Eddington (1926), Regener (1933), Nernst (1933), McKellar and Herzberg (1941), Finlay-Freundlich (1953) and Max Born (1953). These authors had predicted temperatures going from 1,9 to 6 K (Andre Koch Torre Assis and Marcos Cesar Danhoni Neves - 1995). Moreover, the forecast, in 1953, by Gamow, of a Cosmic Microwave Background Radiation at a temperature of 7 Kelvin degrees, was founded on a fallacious mathematical argument (Weinberg 1980)

2) if the model of Hot Big Bang can explain the origin of the fossil radiation, the problem of the horizon remains on account of the quasi-uniformity of the Cosmic Microwave Background Radiation. Only the inflation model, without experimental base, seems to be able to provide a highly speculative answer to it.

3) the smallness of the fluctuations of the fossil radiation is insufficient to justify quantitatively the formation of the galaxies and the great structures of the universe.

One of the major arguments of the model of Hot Big Bang is the synthesis of the light elements a few minutes after Hot Big Bang. It is the standard model of the nucleosynthesis of the Big Bang (Nucleosynthesis Big Bang). This primordial nucleosynthesis, characterized by the primordial abundance of the light elements, depends on the initial conditions of only one free parameter, the ratio Eta baryon/photon. This ratio is currently estimated between 4,5 and 4,9 10-10 (Trento 1997).

In the first three minutes following Hot Big Bang, the cores of the light elements were created from baryons: 2D, 3He, 4He and 7Li (Weinberg 1980). Current abundances of these elements, compared to hydrogen, are: 2D = 4,9499624 E-5, 3He = 1,3265581 E-5, 4He = 0,24387701, 7Li = 1,8648816 E-10 (Craig Hogan - Shine Mendoza 1998). The heavier elements will be created later on in stars.

The agreement of the forecasts of abundances of the light cores starting from the basic assumptions of Hot Big Bang and current abundances of these cores would constitute a strong point of this model. One must indicate that there are many versions of not-standard scenarii of Hot Big Bang. Thousands of articles were devoted to it. They are based on initial conditions of Hot Big Bang different from the standard model (primarily the ratio baryon/photon but also with other assumptions like inhomogeneousness, properties not-standard of the neutrinos, etc...). Nevertheless, all these models are based on the model of Hot Big Bang, but with different initial conditions.

1) The origin of the creation of lithium, a few minutes after Hot Big Bang, is discussed. An unexpected origin of lithium was discovered in the red giants of a dozen globular stars clusters. It would come from the disintegration of the unstable radioactive isotope of 7 beryllium. One also finds lithium in other red giant stars of great mass, at a late stage of their evolution (Catherine Pilachowski 2001). Besides one is unaware of the number of lithium produced before the formation of the stars and how much were destroyed in stars.

2) There is discordance between the B.B.N. forecast values for deuterium 2D and the observations of researchers (Trento 1997). The figures for 4He would be 0,246 ± 0,0014 for Burles and Tytler and 0,234 ± 0,002 for Olive, Steigman and Skillman (OSS 1999). For the ratio baryon/photon, the discordances would be between 5,1 ± 0,5 10-10 (Burles and Tytler) and 2,1 ± 0,6 10-10 (OSS).

3) According to the cosmological standard model, the density baryon, a few seconds after the Hot Big Bang, have a value ranging between 3 and 5 %. According to the cartography of fluctuations observe by the collaboration Boomerang (2000), in the cosmic background noise of 300.000 years after the Hot Big Bang, the density baryon would be of 7,4 % (± 1 %). This discordance casts the doubt over the standard model of the Big Bang Nucleosynthesis.

The age of the universe constitutes an essential element of the model of Hot Big Bang. It cannot be unmatched with the standard model of Hot Big Bang.

There are at least 4 independent ways to measure the age of the universe: 1) the expansion of the universe and the constant Ho of Hubble 2) the age from the oldest white dwarves 3) the age of the chemical elements 4) the age of stars of the globular clusters.

1) The expansion of the universe - the last statistical estimates of the constant of Hubble Ho give a value ranging between 66 and 82 Km/sec/Mpc (G.F.R. Ellis). A recent analysis of Allan Sandage gives a value of 47 Km/sec/Mpc. Nevertheless, the most probable Ho value would be currently 72 Km/sec/Mpc. In the flat universe which is dominated by the ordinary or dark matter, implied by the theory of inflation, the age of the universe is equal to the inverse of the 2/3 of Ho is approximately 9 billion years. If the universe has a very low density of matter, To = 1/Ho is 12 to 15 billion years (MAP 2001)

2) The age of the oldest white dwarves is estimated at 11,5 billion years (Edward L Wright 2001).

3) The age of the universe can be estimated starting from radioactive chemical elements, in particular rhenium 187 which is transformed into osmium 187 with a half-life of 40 billion years. According to a model of formation of the chemical elements, one leads to an age of the universe from 11,5 to 17,5 billion years (Edward L Wright 2001).

4) The age of stars of the oldest globular clusters is estimated at 16 or 17 billion years, after the corrections made to the distance scale in the universe by measurements of the Hipparcos satellite of the ESA (1997): M 92 (Hartmurt Frommert - Christine Kronberg 1999) - M 15 (Leos Ondra 1998).

1) If it is considered that the universe is flat, according to predictions of the inflationary model and last measurements of the experiments Boomerang and Maxima (MAP 2001), the age of the universe would be 9 billion years. This age is seriously unmatched with independent measurements by the radioactive elements and the globular clusters. Let us note that the " quantum " value of To, established by the author in 1962 corresponds to a constant of Hubble Ho, of 67,71 Km/sec/Mpc (approximately 14,43 billion years). The most probable value, today, after decades of revisions, of constant of Hubble Ho, deduced from the expansion of the universe, would be 72 Km/sec/Mpc (approximately 13,6 billion years). The last data given by WMAP ( February 2003) made it possible to fix the value of the constant Ho of Hubble at 71 Km/sec/Mpc ( with a margin of error of 5 % ) what well confirms the temporalist value of Ho is 67,71 Km/sec/Mpc. ( http://map.gsfc.nasa.gov/m_mm/mr_limits.html ).

2) The age of the universe, evaluated starting from the age of the radioactive elements is in disagreement with the low estimate (9 billion years) of the age of the universe and even possibly of the high estimate (13,6 billion years) with a fork from 11,5 to 17,5 billion years.

3) The age of oldest stars of the globular clusters (M 92 and M 15) is in disagreement with the low and high estimates of the age of the universe measured by the expansion (9 and 13,6 billion years for 16 to 17 billion years). Even after the modifications of the distance scale (Hipparcos satellite 1997 - Hartmut Frommert - Christine Kronberg 1999).

4) The most remote supernova ever detected, 1997 ff, dated of 10 billion years, in the childhood of the universe. However this supernova is located in an elliptic galaxy, with a very weak glare and of red color. This redness is due to the billion old stars which constitute it. How old stars can exist some time after Hot Big Bang (Adam Riess 2001)?

The geometry of the universe, according to the general theory of relativity, is determined by the density of the universe. For the critical density omega = 1, the universe is flat. For a density < 1 the universe is opened and for a density > 1 the universe is closed. The theory of inflation implies a flat universe with a density almost equal to the critical density omega and a non-null cosmological constant. The density of the universe is estimated at 0,1 in the galaxies and 0,5 in the galaxy clusters and the broad structures (K. Ratnatunga - R.Griffiths 1998). The dark mass of the universe is evaluated at 90 % in the galaxies and 99 % in the great structures and would be made up of hot dark matter (of mass 0, like the neutrinos?), maybe of cold dark matter (white dwarves, neutron stars, black supermassif holes, brown dwarfs, Machos - Massive Compact Halo Objects -, WIMPs - Weakly Interactive Massive Particles, etc...).

The hierarchy of the scales of structures of the universe goes from the average distances between stars (1 Pc = 3 10^18 cm), galaxies (1 Mpc = 3 10^24 cm), galaxies clusters (10 Mpc = 3 10^25 cm), superclusters of galaxies and voids (100 Mpc = 3 10^26 cm), great structures - walls and filaments - (150 Mpc = 5 10^26 cm). The Great Attractor, located at 65 Mpc (2 10^26 cm) of the earth, in the direction of the Centaurus constellation, attracts a river of galaxies which includes the Local Group, the Virgo cluster, etc..., at the speed of 600 Km/sec.

1) The inflation model implies a flat universe with a density of the universe roughly equal to the critical density omega. However, if the last observations converge towards a flat universe, its density is far from the critical density (0,1 for the galaxies and 0,5 for the great structures).

2) The stars are not randomly distributed in the universe but tend to gather in increasingly vast structures, going from the globular clusters to the large walls and the structures several times vaster. The great structures are separated by regular voids, filling 90 % of space, of typical diameter of 25 Mpc (8 10^25 cm) which can go up to 124 Mpc (4 10^26 cm) (Stephen D. Landy 1999). Nothing, in the model of Hot Big Bang, nor in the inflation model, can give an account of this periodicity of the great structures. We will further see (Chapter 10) that the temporalist model answers it in an adequate way.

3) According to the observations of the HST (Hubble Space Telescope), 10 to 20 % of the most distant galaxies clusters are at 7 billion years.A population of tens and even of hundreds of galaxies is thus assembled early in the history of the universe (K Ratnatunga - R. Griffiths 1998) and even certain galaxies, 2 billion years after the Big Bang (Cambridge Cosmology). This precocity of the great structures is in obvious contradiction with the theoretical predictions of Hot Big Bang.

4) To cross voids of 100 Mpc (3 10^26 cm), at the average speed of 600 Km/sec, the galaxies would take 160 billion years (3 10^26 cm / 6 10^7 cm/sec). The voids and the galaxies are thus located currently where they were created. Which is perfectly incompatible with the standard model of Hot Big Bang, the inflation model and the model of Cosmic Microwave Background Radiation.