Matter
ghost-matter astrophysics.
3
: The radiative era : The problem of the "origin" of the universe.
The problem of the
homogeneity of the early universe.(p2)
Matter ghost
(twin) matter astrophysics
3 : The radiative era :
The problem
of the "origin" of the Universe
The problem of the homogeneity of the early Universe
J.P.Petit &
P.Midy
Observatory of France - Centre de calcul d'Orsay
France
Abstract :
We take the system of two coupled field equations and focuss on radiative
era. We assume that R = R* . In order to avoid the trivial solution R »
R* »
t we apply a the variable constant model, presented in former papers. Then
we get a model in which the constants of physics vary during the radiative
era, then tend to absolute constants over the matter era. During the radiative
era the entropy per baryon is no longer constant. The horizon varies like
R, so that the homogeneity of the Universe is ensured at any time in the past
: Inflation Theory is no longer necessary. We introduce a basic clock, composed
by two masses orbiting around their common centre of gravity. Time is identified
to the number of turns. We find that our clockmade an infinite number of turns
in the past so that the so-called "origin of the Universe, and t = 0
point" become questionable.
- Introduction
In former papers ( [1]
& [2] ) we have introduced
a cosmological model based on a two-folds cover of a manifold (or on a two-points
bundle of a M4 manifold, which is equivalent). We assumed it was governed
by the following coupled field equations system :
(1)
S = c ( T - T*
)
(2)
S* = c ( T* - T
)
with :
(3)
T = Tr + Tm
(4)
T* = Tr* + Tm*
Obviously :
(5)
S* = - S
where S and S* are geometrical tensors. The index m refers
to matter while the index r refers to radiation.
Fig.1 : The joint evolution of matter and ghost
(twin) matter.
On figure 1 we see that the two scales parameters depart from
linear evolution, due to gravitational instability. The expansion of the ghost
(twin) uiverse becomes slower and it pshed ours, whos expansion accelerates,
so that the twin Universe behaves like a "cosmological constant".
We assume discouplings between matter and radiation occur at the same moment
in both Universes. In addition we assume that, during the radiative era :
(8)
R = R*.............. p = p*..............
r = r*
In references ( [4]
,[5] , and [6]
) we developed a model with"variable constants", applying
both to radiative and matter eras, but this model introduced different gauge
processes for gravitation and electromagnétism. Fora example, le mass
was found to follow :
(8)
m »
R
while the electric charge follows :
(9)
The Rydberg constant (ionization energy of the hydrogen atom)
obeys :
(10)
Ei »
R
which gives the redshift. The Jeans and Schwarzschild lengths
vary like Rwhile the Bohr radius was found to obey :
(11)
which, as notices later by collegues, would arise a severe problem
for electron anti-electron pairs creation-annihilation. In the following we
reconsider this model, applying this concept of the variable constants to
radiative era only. Then, during the matter era the constants behave like
absolue constants. We have no redshift on photons emitted before the radiative
era, which is not a problem, for we cannot evidence it. Before discoupling
the Universe is optically thick.
- A model with variable
constants.
The so-called constants of physics
are :
(12)
c : light velocity
(13)
G : constant of gravity
(14)
m : masses (neutral and charged
particles)
(15)
h : Planck constant
...Plus other constants, from electromagnetism
:
e : electric charge
eo
: dielectric constant of vacuum.
...G
and c are linked through Einstein constant :
(16)
...As
shown in reference [4] Gand c may vary in time if :
(17)
Instead writing :
(18)
x° = co
t
where co
is an absolute constant, we may write :
(19)
x° = c(t) t
...A solution of the Einstein equation is an
hypersurface. A solution of our field equations system is an hypersurface
composed by two folds (the involutive mapping was described in [1] and [3]).
In both cases we "read" these solution through an arbitrary choice of coordinates,
where r is identified to a radial distance and t to cosmic time. The choice
(19) must fit the matter dominated era solution (from the former paper [2]).
It is possible if our "variable constants"c(t) , G(t) , h(t), m (t), e(t)
, eo(t)
tend rapidly to their today�s values, immediatly after radiative era :
(20)
Go
(gravity) , co
(light velocity) , mo
(masses), ho ,(Planck)
(21)
mo,
eo
(electromagnetic constants)
- How to determine the
time evolution of "variable constants" set.
G(t) and c(t) are coupled through
(17) to fit the zero divergence condition. Physics depends on a certain set
of basic equations (which are not all independant). We assume that the variations
of the "constants" of physics, during the radiative era keeps all these equations
invariant.
Schrödinger equation :
(22)
Boltzmann equation :
(23)
where f is the distribution function of the velocity v , of the position
r = (x,y,z), t the time, (g, a, w)
the classical impact parameters of a binary collison.
(new) Poisson equation for gravitation
[1] :
(24)
Df =
4 p G
( r - r*)
Maxwell equations :
(25)
(26)
(27)
ї
. B = 0
(28)
(29)
where re
is the electric charge density
and Qthe cross-section :
(30)
...We
put all these equations into a generalized adimensional form, considering
that the constants can vary. We introduce lenth scale factor
Rand time scale factor T
.
(31)
...In
Schödinger equation, we can write :
(32)
Schrödinger equation becomes
:
(34)
Its invariance will be ensured
if :
(35)
where h , m , R , Tare treated
as variable quantities.
...For
the Boltzmann equation, we write :
(36)
v = c z.....
r = R x.....
g = c g .....a
= Ra
and :
(37)
In Boltzmann equation there is
a force term, defined as the gradient of a potential
f. Writing
:
(38)
(we assume that the number of species is conserved)
...Boltzmann
equation becomes :
(39)
Its invariance is be ensured if :
(40)
which mixes the space scale factor
R, the time scale factor Tand the "variable constants" G , m and c . We get
:
(41)
R »
c T
and
(42)
