W. PETRY 25

5. A New Interpretation

In this section a new interpretetion of the results of sec-

on 4 is given. All the fo rmulae and results of the previ-

nterpretation of a bounce,

ng universe. This is pos-

whereas the total energy is conse

La

ti

ous chapter are valid ex ept the i

i.e. of a collapsing and expandi

sible by virtue of the conservation of the total energy (28)

with (24) and (26) in flat space-ti me theory of gravitation.

The universe can be interpreted as non-expanding where

the redshift follows by the transformation of the different

kinds of energy into one another (see [14,15]). The for-

mula for the redshift is identical with the one of the ex-

panding universe. The derivation of this result can be

found in [13-15].

In the beginning of the non-expanding universe, no

matter, no radiation and no dark energy exist by virtue of

(31) and (55). In the course of time radiation, matter and

dark energy arise rved.

ter on, matter and radiation decrease (this corresponds

to the expanding universe). Formula (24) for matter with

(57b) implies that matter is exponentially decaying for

sufficienly large proper time

in the non-expanding

universe analogously to the radioactive decay whereas

dark energy increases to a finite value as t, respctively

goes to infinity. It is worth to mention that this result

depends on the assumed dark eergy given by a cosmo-

logical constant. For 0 , again no matter and no ra-

diation exist in th e beginning of the universe. Matter and

diation arise in the non-expanding universe and matter

increases to a finite value whereas radiation goes to zero

in the course of time. Ttal energy is again conserved

(see, e.g. [11,12]).

It seems that a non-expanding space is a more natural

interpretation of the universe implied by the use of gra-

vitation in flat space-time. The problem of velocities of

galaxies higher th

n

ra

he to

an light velocity doesn’t arise and

so

models. The u

lar, i.e., in the beginning of the

r on it expands for all tim

pretation by the use of flat space-time theory of gravita-

tion than an expanding space. Here, th

axies is explained by the change of the different kinds of

energies in the course of time where the total energy is

wald, Physical Review Letters, Vol. 86, 2001, pp.

5227-5230. doi:10.1103/PhysRevLett.86.5227

mething like inflation is superfluous because in the

beginning of the universe, no matter, no radiation and no

dark energy exist, i.e. all the energy is in form of gravita-

tion and the space is flat for all times.

6. Conclusion

The theory of gravitation in flat sace-time is applied to

homogeneous, isotropic, cosmologocalni-

verse is non-singu

verse space contracts and lateuni-

es.

A non-expanding universe seems a more natural inter-

conserved.

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