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What says to us the uniformity of the sky on the creation of the World?

An evident observation such as the uniformity of the space in two opposite directions asks of profound questions on the primitive time of the universe and the phenomenas which occurred before these separate places were separated.

At first are exposed the characteristics of the infrared cosmological background radiation, which informs us exactly about the degree of uniformity of the young universe, and to expose the general lines of a theory allowing to explain this extreme uniformity.

Then is exposed the link between the topology, that is the global shape of the space, and its contents, what brings up the problem of the finite or infinite dimension of the universe.

Finally, and in a rather speculative way, are evoked the questions turning around the link between the structure of the universe and the expansion as well as the relation, by the conservation of a critical density, between the observable horizon of the universe and its global contents.

1 The cosmic microwave background radiation
2 Curvature and inflation
   2.1 Curvature
    2.2 The geometries of time-space
    2.3 Topology and finite versus infinite universe
    2.4 Evolution and inflation
3 The original substratum

1 The cosmic mocrowave background radiation

The horizon of the observable universe is for a distance of 15 billion light years. The size of this visible universe was 10 million light years during the emission of the Cosmic microwave background radiation In this time, the universe had had no time to homogenize. Now this stream is isotropic, that is identical in all the direction.

How can 2 places without relations before today be so alike?


In 1964, Penzias and Wilson  discovered the Cosmic Background Microwave Radiation ( C.M.B. ), this centimeter radiation bathing all the universe and corresponding to the emission of a black body perfectly absorbing in 2,73K. This emission is due to the expansion of the universe. The increase of the radius of curvature increases the wavelength of photons. These photons were coupled with the matter  which  absorbed them and re-emitted them constantly. Hence, matter and photons have the same temperature

The temperature fell and, when the threshold of 3000 K was reached, there was sudden increase of the number of atoms formed by coupling of electrons and light pits (hydrogen and helium essentially). Photons emitted previously were constantly in interaction with the free electrons reducing strongly their free course and conferring a thermic character on the brilliance by its multiple interactions (the absorbed energy is remitted with the same energy and there is impossibility to reconstitute trajectories). The matter thus constituted the walls of this black body a priori perfectly absorbing.

When atoms were able to form in big number, the effective section of the bound electrons being 500 times lesser than that of the free electrons, photons were then able to cross the matter in a straight line and the universe became transparent. The free average course of photons change suddenly of 3000 years, very insufficient to cross all the universe without interaction, in 300 million years and this free course continued since to grow slowly with the dilution of the matter and the reduction of its interaction with the radiation.

The decoupling also corresponds as the density of radiation crossed under the density of the matter. It occurred from 300 to 700 000 years after the Big-Bang.

The fundamental level of the hydrogen (13,6 ev) corresponds to a temperature of 160 000 K reached only a century after  the Big-Bang. But at this temperature the amount of bounding energy  which is realeased by the forming of atoms stay  weak. The system which tends to maximize its numbers of states thus keeps a total ionization until a temperature of 4800K and the majority stay ionized until 3400 K.

We can also consider another factor, that of the dispersal of the energies due to the quantum statistics which maintained, up to the final decoupling, a proportion of high-energy photons which destroy the formed atoms.

By considering far, we observe more and more former light sources. These sources undergo a gap of the frequencies bound to the differences of curvature of the universe between the emission and the reception.

This gap of curvature also played on the C.M.B.. We can so discover the effect on young galaxies of a warmer cosmic microwave background radiation ( 10K ). Beyond 15K, the universe has less than 1 billion years and there were no galaxies, not even no stars. The only ones of clouds cold of diatomic hydrogen still to discover could interact with the C.M.B. in these dark ages.

But in theory if there were essential structures, we could observe the effect on the C.M.B. until very remote times. This one was emitted when the radius of universe was 1100 times smaller than  today since the C.M.B.  varied from 3000K to 2,73 K
The study of the spatial variations of the C.M.B. so informs about the  slight overdensities  which could be present at the time of  emission,  these  structures could
possibly be the product of a hypothetical black matter incapable to diffuse photons and thus not scattering under the radiation pressure.

This C.M.B. acts as a barrier of the information: we cannot see farther behind (so far as  electromagnetic radiation is concerned) because the universe becomes opaque.

The knowledge of  primitive unhomogeneities and thus structures of the primitive universe is almost refused to us.

In fact the C.M.B. is not an absolute barrier because statistically certain photons managed well to cross the barrier of the absorbent ions (more and more rarely when we go back time and increasing  the density and the excitement of the ions).

The thermic balance between the matter and the radiation is maintained only one hour after Big-Bang (until T~130 millions of Kelvins). Then, the interactions did not modify any more the number of photons but only their energy in the progressive cooling. After 1000 years of expansion, the balance began to break and the most energy photons were not absorbed any more as well by a less dense matter; the profile of black body was not any more completed. At the age of 300 000 years the decoupling was reached ) and there were no more sufficient interactions to deform the spectre of black body the profile of which remains unchanged until us. Only the characteristic temperature of photons simply continued to slide by the expansion of the Cosmos and the variation of its radius of curvature.

The measure of the intensity of the curve in the various wavelengths thus inform about the various processes which release photons for the 1 hour after Big-Bang until today. This ascent is quite theoretical and the ultimate barrier seems to be one thousand years.

On the other hand, the angular distribution informs about the structures perturbing the homogeneity of the stream.

Variations of the C.M.B. were discovered by the satellite Cobe in 1992. The simple effect of the movement of our galaxy engenders a variation only of 3,4 milliKelvins . Beyond the variations were discovered at the level of a percent one thousand (the wrinkles of time according to the work of G.Smoot). These variations are insufficient to engender galactic structures within a billion years, this duration corresponding to the cosmological gap of their spectre. It is thus necessary to bring in a hypothetical black matter, not sensitive to the electromagnetic interaction, and which would have created the germs of the galaxies from the first thousand years without that these germs perturb the isotropy of the C.M.B..

The C.M.B. reaches us of a sphere centred on the observer and whose radius is given by the difference of time in light years between the time of emiision (300 000 years after Big-Bang) and the time of reception (15 billion years)

This C.M.B.  is not as a front of wave which arrives on us and exceeds us. Because Big-Bang arose completely of the universe, the C.M.B. which will reach us in one year was emitted by a concentric sphere the radius of which is 1 Y.-L. superior to the radius of emission of C.M.B. at present successful.

The difference of radius of curvature will have still increased the wavelength and reduces the temperature of 1/15 of billionth

There is no space in the universe where Big-Bang did not take place because it is the creation of the matter and its expansion which created the space the packaging; there is no pre-existent or definable space independently of the contents.

Because the radius of the observable universe extends, more and more primitive galaxies appear and the front of wave of the C.M.B. extends. The horizon is pushed away and a more and more important fraction of the real universe appears to us as our glance dives into this total space bigger than our observable space.

This space is also homogeneous as our closer space. The proof: the C.M.B.. received from 2 opposite directions is perfectly homogeneous and always corresponds to the emission of a black body with a temperature of 2,73 K.

How the universe  evolved since the C.M.B. emission ?

Our phase of the universe is said era of matter, by opposition to the previous era of the brilliance, because the density of energy of matter prevails over the density of energy of the radiation (even if in number of particles there is 1 billion photons for 1 particle of matter).

The conservation of the energy, the sum of the kinetic energy and the potential energy of gravitation, implies that in this era of matter the radius is multiplied by 4 when the time is multiplied by 8 (and multiplied by 16 before the C.M.B.).

This means that two opposite points of our observable universe (the zenith and the nadir), which are  today separated from a diameter of 30 billions years- light, were still separated from 10 million Y.-L. when  C.M.B. emission took place.

This event having occurred approximately 300 000 years after the big-clap, how the points which could not communicate would they have been able to homogenize?

Let us call back that the relativity relies on the fact that two events cannot be synchronized before the information propagates from a point to the other one.

It would mean that points which seem to return in contact only today by the stream of the C.M.B. underwent, at the beginning of the universe, a synchronous phenomenon which homogenized them.

The quantum physics supplies us with strong indication to indicate the period from 10-35 to 10-33 Second after Big-Bang as the moment of the world history which saw the homogenization of the universe.

2 points separated from 10 million Y.-L.  when t=300 000 years were still separated from approximately 2 metres about  10-33 s after Big-Bang. How this fireball of 2 metres could already  be homogeneous?

It is there that the tour of pass of the quantum physics intervenes. It brings in a "inflationary" process which increased the distance between 2 extremely close points.

The initial universe possesses a size the uncertainty of which was 1,6 10 -35 M and the uncertainty over the moment of the measure is 10-43 second.  It means that in a inflexible way we cannot consider smaller intervals because it is about an uncertainty inherent to any measure.

Fundamentally the universe possesses initially no detectable matter; it is formed by an empty and by definition homogeneous substratum.

Let us develop the universe until time 10-35 second. The size of the total universe is then of the order of 10-25 meter.

It is at this moment when the universe enough cooled so that a phenomenon of internal transition increases its size until approximately a year- light, what is much superior to the initial 2 metres of the today observable universe.

In the term of this inflation, the potential energy of the space is converted in matter and becomes a fireball.

What are the consequences of the inflation?

We know by the general relativity that trajectories are modified by the contents in energy and en masse of the portion of the universe crossed.

This twisting of trajectories is called curvature.

So the universe possesses an average curvature related to its contents in energy.

If the universe possessed initially an intrinsic curvature or if essential black holes created zones locally bent, the fantastic expansion of the vacuum, by increasing considerably the radius of the universe, reduced strongly the variation of a trajectory with regard to that in a vacuum of matter.

It is in the sense that we speak about a flat space.

In the next part we shall examine the sense which is given to the word curvature and the various topology that the universe can set.


The wrinkles of time G.Smoot to Fields Flammarion

Last one news of the Cosmos H.Reeves to Points Sciences

The universe under the glance of time (l'univers sous le regard du temps) H.Andrillat Collection Of Caelo at Masson

2 Curvature and inflation

2.1 Curvature

We saw  that trajectories are modified by the energy and masse contents of the crossed space. It is in fact an interaction between the mobile and its environment, the contents in energy of the space is related to the speed of the mobile.

The modification of trajectories is called curvature. It aims at moving closer to the mobile of the source of the field of gravitation what slows down successively the drainage of time in this direction; the straight lines are transformed into curve. This effect relies on the postulate of the equivalence between gravitational mass and inertial masses .

The curvature is a function of the distance to be crossed(to be gone through). Now this one is modified by the impulse of the mobile (effect of contraction of the lengthes) and by the average energy of the environment (curvature of space-time by the masses).

But let us try to represent geometrically this curvature.

The density of the universe is considered as identical completely. Its evolution is governed by a cosmic time the origin of which is Big Bang and running with the same rhythm in any point .

The universe thus possesses a radius of curvature which is seen equal completely at the moment given of cosmic time. This radius of curvature is a factor of  distance scale between the observer and the point the most remote from the universe.

This universe is dynamic. Its radius of curvature evolves in time (the radius) of the universe increases since Big Bang). It is about a space in three dimensions by which the distances between 2 points increase continuously, what gives the impression of a space to three dimensions plunged into a universe in 4 spatial dimensions but it is about intrinsic properties and there is the fourth spatial dimension, " one somewhere else " in the universe, the distances being the measure of the evolution of the density averages of the universe.

For a homogeneous universe, the curvature is related to its average density and to its cosmological constant. Generally this constant is neglected.

2.2 The geometries of  time-space

There are mathematically 3 types of spaces: the elliptic, the Euclidian and the hyperbolic.

A) Let us consider the Euclidian universe said in no curvature or flat space. This universe corresponds to a critical said density.

In the Euclidian universe, every point P of the universe can be seen as being for the suburb of a sphere of radius R and of centre O, let us clarify at once that there is an infinity of point O for which we are for the suburb of the circle centred on them.

Let us move our point P on the suburb of this sphere of centre O.

We crossed an angle y with regard to the axis OP.

The distance r crossed is Ry.

In the universe of critical density, the circle is not deformed; this circle has the same properties as in a space where the matter would not deform the space.

A universe in 3 expanding dimensions in the course of time and the density of energy of which is optimal possesses the same properties of trajectory as a flat universe in two dimensions without deformation because empty of matter.

This space is equivalent to a flat or Euclidian space.

So the sum of 3 angles of the triangle connecting 3 points of the universe would make exactly 180 °.


Let us consider now an observer who would realize circles the radius of which would be the radius of curvature of the universe. Here is the movement which he would follow. The universe extends continuously but more and more slowly.

B) In a universe with (convex) positive curvature, the circle would be deformed and added angles would be lower than 180 °.

Let us move again our point P on the suburb of this sphere of centre O.

We crossed an angle with regard to the axis OP.

The distance r crossed is R * sine y. and thus lower than the Euclidian case (because the matter is denser and the more deformed space)

In this universe the circle is deformed; everything takes place as if the centre of the circle was not any more O but a point H with a distance R * sine lesser than R

The universe is in that case as an ellipsoid of revolution around the axis OP. If a vessel crossed from P to O and would continue "beyond" the shape of the space would be such as the vessel would return P there.


Let us resume the situation of the observer which would realize circles the radius of which would be the radius of curvature of the universe. Here is the movement which he would follow. The universe extends continuously but more and more slowly (expansion) and restarts the other way around (contraction).


In fact the universe when we observe it in an axis would be as a rugby ball of which we would be one of 2 extremities and single half of which we would see. Other half is in a sense reentrying (folding up)  in the first one.

Why such an reentrying ellipsoid nstead of a simple rugby ball ? In order to protect the uniformity of the space.

Let us leave in front of us and let us cross the universe (let us not consider the expansion which takes away our objective). If we reach its "edge", the space would not be homogeneous any more; the space could be so gone through throughout and who would have it beyond?

On the contrary, the space ellipsoid is folded up; it has no edge which we can reach; any route is totally included in this space and we cannot only return eventually to our initial point.

The reasoning is the same for the Euclidian space and the spherical space which was envisaged must be replaced by a spherical reentrying space . So any route on a hemisphere is followed by an additional route on the other hemisphere, the route folded up inside the first one.

We often associate the universe to positive curvature in a universe which would be denser and thus more bent than the universe of critical density. In fact we shall see that the inflation imposes a critical density. To defend(forbid) a universe of positive curvature means denying the process of inflation.

C) A universe with (concave) negative curvature would also deny the process of the inflation and would suppose a universe less dense than the critical density.

In this universe with negative curvature, the circle would be less deformed by the matter and the sum of angles would be superior to 180 °.

Let us move again our point P on the suburb of this sphere of centre O.

We crossed an angle y with regard to the axis OP.

The distance r crossed is R * hyperbolic sine y ~ R / 2 * exponential y and thus superior to the Euclidian case (because the matter is less dense and the less deformed space)

In the universe of under critical density , the circle is too little deformed; everything takes place as if the centre of the circle was not any more O but a point H has a distance R * hyperbolic sine y superior in R.

The universe seen according to an axis appears then as a hyperboloid of revolution around the axis OP.

This space is comparable locally to the shape of a saddle of horse; it is opened and if it possesses locally a radius of curvature, circles bounded by every point of a trajectory also move and in that case we could not return to our point of departure because this universe do not possess limit distance; it is infinite.


In this last case the observer who would realize circles the radius of which would be the radius of curvature of the universe could not curl a single tour because the universe is always increasing even when we make stretch out the variable time towards the infinity. In certain models bringing in a fast expansion of the space, the growth accelerates even in the course of time.

2.3 Topology and finite/infinite  universe

The topology is the science of the forms that a space can set. Character differential of the equations of the relativity allows only to determine the local impact of the fields of gravitation, even if these solutions are spread to the homogeneous and isotropic supposed whole universe.

The topology, it is-à-to say the global shape of the universe cannot be determined by these equations.

With the simplest topology and thus the most likely, the elliptic universe is a space closed not only in the time (expansion followed by a contraction) but also by the finite dimension of the space.

In the simplest topology, the Euclidian and hyperbolic spaces can extend without limitation (unless they are it already infinite, what is more difficult to admit physically).

But there is the other topology allowing the Euclidian or hyperbolic spaces to be closed. The most coarse examples would be the torus or the cylinder; this Euclidian space can be folded up by its topology in a torus or a cylinder which closes on itself.

For lack of determining the topology of the universe, we could not conclude on a finite or infinite size of the universe that in case the density of the universe would be superior to the critical density.

2.4 Evolution and inflation

The evolution of 3 types of space is characterized by the constant of Hubble which is only a spatial constant but which is not constant in the time. It expresses the report enter the speed DR/Dt of variation of the curvature and the curvature R, at the moment given of cosmic time.

In the Euclidian case, the expansion is continual. The constant of Hubble will aim towards zero only at the infinity; the life expectancy of this universe is infinite.

In the elliptic case, the constant of Hubble aims towards zero at finished time, nullifies then becomes negative; the universe retracts having dilated. Its life expectancy depends on the initial value of the expansion (who could depend on the cosmological constant which is very important at the beginning of the universe).

In the hyperbolic case, the constant increases in time; the life expectancy of the universe is infinite and the density of matter aims towards zero.

The cosmological constant represents the potential density of energy of the space. It is characterized by an internal tension equivalent to a pressure completely increasing the distances and thwarting the attraction, universal of the matter. In certain models, the cosmological constant is so important as the expansion could accelerate in the course of time. This accelerated expansion also characterizes the first common phase of the universe in all the types of space and which precedes the creation of the matter: the inflation.

A field is a potential state of energy completely. Fields can be simply directed (vectorial ) as the electromagnetic field, directed and coupling the dimensions of space two - two tensoriel ) as the field of relativist gravitation, or without orientation (scalar) as a field of temperature.

Knowing that in quantum physical  the sizes cannot quite be equal to zero with certainty, the state of the space corresponds only to a state of minimal energy. We thus suppose that at the beginning of the universe there is a scalar field (field of Higgs) characterizing the state of the space and a field of interaction where all the nuclear forces and electromagnetic are unified.

The dimension of the space determines the wavelengths of the field of interaction which can propagate there, as would make it a guide of wave. For a wavelength we can make correspond an equivalent temperature.

When the dimension of the space crosses(spends) a threshold, the wavelengths which propagate become equivalent in wavelength of the scalar field; we say that the temperature falls under a critical threshold.

It is that in this temperature that the oscillations of the field of the space can influence the oscillations of the field of interaction. A capacity of "friction" of particles in the field of the space is brought; this new capacity is the mass which limits the speed of propagation.

At this critical moment, bosons, vector particles of the fields of interaction, interacting with the scalar field and thus acquire a mass. The reach of the forces becomes not infinite; the field of interaction splits then into strong nuclear and  electroweak fields: there is break of  symmetry.

The scalar field dominating the fields of interactions, the expansion is then characterized by the expansion of the space.

Because the space is by definition, invariant, it extends by keeping its density of energy; the expansion becomes exponential.

The essential inflation increases considerably the radius of the universe and trajectories on a big portion of the universe would be equivalent to those observed in a vacuum of matter.

It is in the sense that we speak about a flat space. It would be advisable better to say that the space possesses three dimensions but that all points being equivalent we can always draw around them the same horizon of visibility, the perfectly spherical horizon of radius of 30 billion years- light for 15 billion years since Big Bang

There is thus no edge and the internal contents of this flat said space are not practically deformed by the masses.

Its radius of curvature swelled excessively; it became so great that it seems locally flat. If the universe was initially in bump (hyperbolic opened) or in hollow (closed ellipsoid), the inflation smoothed all the distances.

In a fraction of a second (10-33 second) The universe would bulged from  10-25 meter  to 10 16 meter (1 Y.-L.) (the initial and final values fluctuate terribly according to the models)

The distance which can exist with regard to the critical density (in more or less) would have been reduced in a exponential way.

How is this possible? A universe with a certain quantity of energy would dilute completely and would not know how to aim towards a critical density.

In fact the universe spreads(widens) its vacuum by the inflation. But the potential energy of the expanding space possesses exactly the critical density. Now the potential energy of the space is connected with 3 fundamental constants: the constant of gravitation ( G ), of Planck ( h ) and in the rate of the electromagnetic waves ( c ). This implies that these constants are adjusted so that the space seems Euclidian.

It is the moment of the conversion between the energy of the space and the energy of the couple matter/radiation which stops the inflation (passage of the false potential space in the true actual space coexisting with the matter)

At the end of the inflation the constant of Hubble is only factor of the density of the space; the universe possesses no more intrinsic curvature on the scale of the visible universe. The gravitation is since then going to have as effect to reduce the constant of Hubble at the same time to the decrease of the density of mater and radiation.

An important point: any distance with regard to an Euclidian universe can not be detectable if the portion of the universe that we discover ( the horizon) is much lower than the radius of curvature. Even in the current time, the observable scale would indeed be below the scale of curvature.

The growth of the observable horizon is made in the speed 2c (this rate is a relative movement between two points; the observer and the limit of its horizon).

Let us remind that if the universe possesses a critical density then we find a size of 15 billion years for the " constant of  Hubble " observed by 65 km / / Mégaparsecs.

You should not thus confuse  the radius of the observable horizon 30 billion years - light for T=15 billions and the radius of curvature of the universe which is considerably bigger.

The observable zone of the observable universe increases in the rate 2c but the radius of curvature of the universe varies of a factor 2 when the triple time.

In time 10-33  second, that is just after the inflation the total dimension of the universe could have been 10 billions of A L (a size close to the part of the present observable universe)

At the time of the C.M.B. to T=300 000 the years, its dimension would be   2 10 15 Y.-L..

In the current time in in T=15 billion years, its total dimension would be 8 10 48 Y.-L..

At the same time what will become our today observable universe was only 2 metres for T=10-33

This space made 10 million years- light to T=300 000 the years and 30 billion years light in T=15 billions.

By comparing the 30 billion years light visible to 8 10 48 Y.-L.of containing and supposed universes homogeneous, we cannot wonder that the horizon of the C.M.B. which extends all the time homogeneous house.

In t = 8 10 77 Billion years, the visible horizon will cover all the universe which will have extended over 3 10 95 Y.-L.

At this moment all the stars will have gone out and will not remain more than the weak radiation of the galactic black holes dissipating slowly. There will be no more anybody and anything more to see.

3 The original substratum

The universe before being material was constituted only by the "empty" substratum an environment constituted by interacting particles , which comes out from a space without limit of negative energy and who acquire a positive energy only the time allowed by the relation of Heisenberg (more energy fewer time). No physical system can discover these particles because these particles propagate only on a single wavelength; any interaction between 2 real particles engenders the appearance of virtual particles which disappear from reception. The effect of these particles, even indirect, must be integrated into the models but their time of existence are below our.

In brief, the substratum being constituted by a potential of negative energy is not related  to the relativist limitation of distribution of the information; its property is remarkable (its density of energy is constant because the well of available energy is without limit). If it is filled with energy, its volume increases in an exponential way (of a factor 1030 In 10 100).

So the total universe produced by this inflation is immense and much bigger than the portion of the universe which will become our visible universe. And this total universe was homogenized by the inflation (quite as a wrinkle disappears during a good face-lift).

Result our portion of observable universe and total universe are going to grow at the same time

Both points initially joint are both extremities of a diameter of the observable universe today but we notice that their immediate environments at the time of the creation of the C.M.B. were similar because they homogenized at the beginning of the universe.

How can the universe during the process of inflation extend initially in a superior rate at the speed of light?

The question is badly put. It is not about a bubble which swells. It is rather about the appearance, about the appearance of a bubble filled with energy. There is no distribution for a powder trail.

The question is to know where from comes this energy and how the appearance occurs?

A first theory evokes a field of potential energy existing a priori, this field would define a state of potential space full of energy, a false space. The inflation would allow the passage a state of actual space, the difference of energy being converts in real particles. The essential bubble would inflate until become almost flat and would thus affect a critical density with an extremely weak distance. This allows that nowadays the difference remains weak and that the density is just sufficient to close the universe, or at the most 10 times too weak in the worst estimations.

But where from would come this essential field and how this unexcitement of the space  would initially have propagated?

Let us note before going farther than saying that our universe possesses a critical density means saying that it forms globally the inside of a black hole. This can seem surprising but the density of a black hole decreases in the cube of the radius; a big universe is thus very diluted. Say that it is of the size of our universe, mean saying that the universe has a critical density.

Question why is this density only that of the observable universe and not that of the total universe? This privileges the first theory of a critical universe by simple extension, without giving a particular sense to the critical density..

A much deeper vision of the beginning of things is allowed by the theories of big unification of the fundamental interactions. Every interaction would be the effect of the withdrawal of a space of superior dimensions.

The beginning of the universe would be seen itself the withdrawal of seven dimensions different from space-time.

The action of this withdrawal would be the transformation of the essential peculiarity in an expanding dilated space, the messenger of this transfer being what the physics call energy.

When the space reaches a potential energy equivalent to the critical density, it possesses then a density which provides the properties of a black hole and this potential of virtual particles is transformed into real particles (quarks,  leptons). But our universe always possesses this critical density.

The critical density is not thus the effect of a universe which become globally flat because of the dilution. On the contrary, the outcome in a critical density completely inferred the unexcitement.

The critical density is not thus an indirect effect, it is the threshold which immediately achieves provoke the fall of the potential energy in real particles.

The energy injected in our space also introduces the notion of time because the time is a measure of the transitions of energy. The time is the measure of the probability of transition from a state to the other one, the probability realted to the differences of energy between 2 states.

The withdrawal of supplementary dimensions would have inferred the creation of this space full of virtual particles and would be converts in a display of space-time.

We understand while this transfer between different dimensions is not related to the properties of our space-time and can come true independently of the notions of rate.

The relativity is based on a purely geometrical approach of the physics, the energy is nothing else there than the value of the curvature of space-time, the limitation of this notion lies in the approach of the universe as a continuous shape. The introduction of the quantum discontinuities engenders a vague texture of the time-space and introduces a limitation into the precision of two simultaneous measures of coupled parameters (for example the position in the time and the energy of a particle).

The notion of speed of propagation is fundamentally connected to our space-time. The quantum physics introduces the possibility of a coupling between two quantum numbers , parameters affected to the particle, coupling which is independent from the distance " as if the coupling propagated faster than the light ". But a phenomenon of censorship engenders the destruction of the information at the time of its measure; the result is completely determined by its measure. Immediately the size measured on the first particle is modified on the coupled particle. The introduction of the interactions fundamental as the demonstration of supplementary dimensions leads to envisage the propagation of quantum parameter according to roads outside our space-time.

Let us imagine a universe where 3 spatial dimensions would be of the minimal size allowed by the quantum physics below this size the universe is absolutely unstable in part the relativity it is transformed into black hole.

In part the quantum physics, the universe is statistically delocalized and its probability to be outside of this dimension is bigger than to be inside.

It is difficult to encircle the space. The introduction at the beginning of the twentieth century of the constant of Planck led to the development of the notion of a "space" full of potential energy.

In fact, it is not any more a question of defining an ether support of the distribution of the material bodies but rather of unterstanding the link between the material bodies.

The fertile introduction of a symmetry in the theories of particles led to the definition of interaction, vector of this symmetry.

These interactions propagate in an environment likened to the vacuum , meaning a space without matter where the information is transported.

But the existence of the Planck indistinctness  on the distances and the energies leads to the relocation of the particles which are rather the place of the cloud of virtual particles surrounding the singular heart of the particle. These particles possess an all the denser energy as they are close to the heart. More the resolution is fine more the spectre of the particle multiplies.

 Therefore particles exchange between them a particle support of interactions. Unlike the particles of  matter subdued to the laws of exclusion, the vector particles of force can accrue without limitation of density.

The real universe is bigger than the visible universe and it is in the same way homogeneous.

How can we consider only the visible universe as a black hole and the outside universe as outside of the black hole knowing that they have the same density at any moment of cosmic time?

In fact, the increasing space, to say that it possesses a critical density means admitting its expansion in a space in 4 dimensions. At the same time, it acquires new  mass by extending in the outside space: 2 masses, the one who was visible and the one who becomes him, benefit from the visible expansion of the universe in a  4 dimensions space.

The visible universe can be thus considered at any moment as an expanding black hole:

The intensity of  C.M.B. decreases and stretches towards zero Kelvin when all the fronts of wave coming all the points of the total universe will have exceeded the observer.