In today’s cosmology the inflationary flat 
-CDMmodel coming out from a big bang (standard model) is widely accepted as the best model of our universe. Although in this model most observations are well matched there are nevertheless some serious problems.
Firstly: The big bang is out of physics and a source of some unsolved problems.
Secondly: The huge cosmological constant driving inflation must fall off within a tiny fraction of a second to the extremely small value we observe today where the inflaton field gives off its energy into reheating the matter. Up to now no consistent field theoretical model has been found to describe this process.
Thirdly: A positive cosmological constant according to 
may explain the small deviation of the redshift-versus-distance relation from that for
. On the other hand such a constant leads to problems in galaxy clusters. As shown in ref. [
This leads to an additional force between two masses which increases linearly with the distance of the masses (repulsive for 
and attractive for
). In refs.[1, 2] it has been shown that the masses and mean distances of galaxies in clusters have just such values that this additional force plays an important role. More precisely, in case of 
with 
which means 
the repulsive forces between the galaxies are so strong that the clusters could not exist unless the content of uniformly distributed cold dark matter is greater than five times the content in the standard model. This, however, would close the universe and lead to an age problem. In other words, the standard model seems to be not consistent.
Fourthly: The standard scenario of galaxy formation is based on the paradigm of cold dark matter. Cold dark matter goes lumpy rather rapidly, and the lumps attract the baryonic matter. Latest observations, however, show that galaxies with their first star population have existed already some hundred million years after the big bang
, and it seems to be questionable whether the cold dark matter scenario can explain this. Moreover, up to now this kind of matter has not been found.
Finally: It is generally claimed that the peaks in the CMB correspond to acoustic oscillations in the photonbaryon plasma before recombination and that the positions of the peaks in the power spectrum favor definitively a flat universe. However, in ref.[
does not represent the fundamental acoustic oscillation, neither in a flat nor in an open universe. Thus the main argument for a flat universe, which is an outcome from inflation, seems to be not valid. In addition it should be noted that also the work by Bose and Grishchuck [
In recent years some efforts have been made to understand the big bang as a bouncing point of a cyclic universe. Ashtekar et al. [
with a potential
, the prime in Equation (3c) the derivative with respect to the argument and 
a flat, closed and open space respectively.
and
. As shown in ref.[
.
and
.
anti-deSitter space with the negative cosmological constant
and 
so that the potential (2) reads
is conserved in the geometrical phase transition, where
in the wrong vacuum is broken down to 
in the true vacuum, and the 10-parametric isometry of the Minkowski space is broken down to the 6-parametric isometry of the antideSitter space.
which is positive as long as
. In refs. [2, 7] a phenomenological model describing the creation of matter and radiation from this positive gravitational energy supply is presented. It is based on the fundamental law of energy conservation, that means that the sum of the gravitational energy density, the energy densities of created matter and radiation and the density 
of dark energy is constantly zero as after the phase transition, hence
) and radiation (index
) is described by the two equations
and
. The first terms on the right hand sides of these equations correspond to the conversation laws 
and 
respectively. In these equations matter means normal matter with non-vanishing rest mass and infinite lifetime (protons, electrons, neutrinos) and possibly cold dark matter. However, in the following we exclude cold dark matter (see Section 1 and the discussion of a universe without cold dark matter and with a negative cosmological constant in Subsection 2.4).
and 
are calculated. It turns out that in a universe becoming later our universe with a present day density 
(purely baryonic, from big bang nucleosynthesis [
and a cosmological constant
with 
the present day scale factor. Furthermore, the creation functions 
and 
become zero at
. This can be interpreted as a smooth transition of the universe from the creation era to the conservation era at
. And it seems to be obvious that this transition takes place when the gravitational energy density becomes zero, hence
and
.
and a nucleon density 
which is about four times the density of nucleons in atomic nuclei.
is not the final state of matter but the preliminary stage of a phase transition to a quark-gluon plasma. This phase transition begins when the hard cores of the strong nucleon interaction start to overlap. In ref.[
is an Einstein-Boltzmann gas running within the time down to 
into a state very close to collision-dominated equilibrium. This state is characterized by extremely sharply bounded gas clouds although the anisotropies of the CMB are extremely small. These clouds have formed about 4 million years (!) after the big bang. Moreover, the mass spectrum of axially symmetric clouds agrees very well observations: The lower limit masses are spheres with 
and the upper limit masses are extremely flat discs with
.
. However, for a present day density 
(purely baronic) and a Hubble parameter 
the redshift-versus-distance relation does for 
not deviate from that for
, at least up to
. Hence, if an alternative explanation for the deviation can be given in case of 
this explanation holds also in case of the cosmological constant (10). Up to now two explanations are possible: Evolution effects of the observed SNIasupernovae (see for example refs. [18,19]) and a very small amount of absorbing intercluster gas and dust. Maybe both effects combine.
which is in agreement with the age of the oldest globular clusters according to the scenario of galaxy formation proposed in ref. [
before the minimum and like a big bang universe the same time after the minimum. This gives rise to shock waves in the coupled photon-matter gas. They are smoothed out when the universe expands and are later the small anisotropies at the end of recombination.
there) the model is for 
the radiation universe of the standard model with its well known nucleosynthesis.
is because of 
the reason why the universe is so big and so old.
and plays a threefold role:
and 
determine the potential 
(Equation (6))
determines the extension of the proto-universe (Equation (5)).
and 
determine the energy content of matter and radiation in the universe (Equation (11)).
with its potential (2) is unclear. There is, however, a difference. The inflaton field is assumed to be created in the infinite temperature of the big bang, whereas the scalar field 
lies “sleeping” in its wrong vacuum state in the zero temperature Minkowski space. Anyway, in both cases the origin of the fields is a problem.