*Repulsive dark matter (p1)*

Repulsive dark matter.

We explore the phenomenological aspects of a two population system whose dynamics implies both attractive and repelling forces. A new geometrical structure, with two folds, associated to two field equations, coupled through the gravitational field, allows to bypass the stumbling block of the "negative masses" and makes such a conceivable system, where the energies of all the particles are positive. We show that in these conditions, the matter in the second population is geometrically non-observable and therefore gets the status of repulsive dark matter. Galaxies would be housed in cavities of a homogenous distribution of repulsive dark matter. This generates a confinment effect with realistic rotation curve. We show that the negative gravitational lensing, associated with repulsive dark matter would explain the strong observed effects, which would be an alternative to the "classical" dark matter model. As derived from this new cosmological model, the age of the Universe becomes 15.7 billions years, due to the interaction of the two matters.

__1)
Introduction.__

** **

...Nowadays trying to account for astronomical
observations on the basis of observable matter only is no longer possible.
That is for dark matter concept has become increasingly widespread. Various
hypothesis have been proposed about the nature of this unobserved component
of the Universe, which should contribute to the formation of the gravitational
field and thus lead to the missing mass effect in galaxies and to gravitational
lensing. Machos have turned out to be disappointing. Some people resort
to particles whose physical existence is speculative, such as massive neutrinos.
In so far no formulation seems to have prevailed and many hypothesis remain
possible about this dark matter. In this paper we propose to investigate
the consequences of a gravitational interaction between our matter (mass
m) and particular dark matter, made of masses m*, such that :

- m and m’ attract each other according to the Newton law

- m* and m*’ attract each other according to the Newton law

- m and m* repel each
other according to a Newton-like law

We shall call m* "repulsive dark matter".

This could
be summed up simply, considering that in the following expression :

(1)

where
the masses ma and mb can be positive or negative. Physicists could argue
immediately, saying that particles with negative masses also have negative
energies, which lacks physical meaning. In the section 3 of the article
we shall propose a new geometrical context which makes possible the interaction
of two populations, with masses m and m*, both positive, whose energies
mc^{2} and m*c^{2} are positive, in such a way that the
forces fit with the former scheme. The fact that the two sub-systems may
interact only through gravitation will be geometrically justified.

.

__2)
Repulsive dark matter confining galaxies.__

...I
has been known for long that the gravitational field due to a matter distribution
inferred from observation would not be able to balance the centrifugal forces
in galaxies. The missin mass is about three to five times the observed one.
Moreover, the rotation curves of galaxies show a characteristic step (peripheral
excess velocities) which cannot be accounted for starting from the observed
distribution of matter. So people attempts both to prevent explosion of
galaxies and to reproduce this aspect of rotation curves using ad hoc, artificially
introduced distributions of dark matter. Let us now turn to the proposed
model of ordinary (observed) matter and unobserved repulsive dark matter,
and see whether this model can ensure the confinment of galaxies. At first,
we consider a galaxy where matter is distributed according to the model
of Myamoto and Nagai [1] :

(2)

...This axisymmetrical matter distribution is supposed to be located in a hole of a uniform repulsive dark matter distribution (Fig.1, in which ordinary matter is distributed according to a = 5 ; b = 1 in (2).

** **
**Fig.1 : The
galaxy surrounded by repulsive dark matter.** **An
axisymmetrical system.**

...We
arrange repulsive dark matter around it, with an ad hoc density gradient,
shaped on empirical grounds. This mass distribution can be described through
a superposition of thick ellipsoids, charged by matter density** **ri
(which could be positive or negative), i being the index of the massive
ellipsoid, with horizontal axis ai and vertical axis bi. The field, inside
and outside such bodies, is given by quite simple analytical formulas ([2]
and [3]). Given a set of such massive ellipsoids it becomes possible to
compute the 3d field. On figure 1 we have figured the mass-density
r*
of repulsive dark matter by the variation of the density of white points
in space. This does no result from numerical simulation, performed with
mass points, as the image might suggest. The mass distribution was described
by a set of massive ellipsoïds, with various parameters (lenghts of
axis, mass-density).

...Figure 2 shows the corresponding chosen axisymmetric repulsive dark matter distribution. Figure 3 represents the gravitational field, due to this repulsive dark matter, computed by the method described above. The two scales of figures 1 and (2-3) are different, the last ones being a zoom. The scale correspondance is indicated. As we can see, the repulsive dark matter distribution produces a confinment effect on the galaxy, both in the r and z-directions. Figure 3 shows the corresponding rotation velocity for repulsive dark matter alone. We see that such a repulsive dark matter distribution allows large peripheric velocities.

**Fig. 2 : The chosen
repulsive dark matter distribution : a set of thick, concentric flat ellispsoids
with density**** **r*(r)
**d being the diameter
of the ellipsoid.**