NeoMinkowskian Cosmological Black Hole, Poincaré’s Gravific Electron and Density of CBR

In the previous paper (JMP 2014) we showed that there exists a NeoMinkowskian Gravitational Expanding Solution of GR (General Relativity) with CC (Cosmological Constant). We prove now that NeoMinkowskian Vacuum (non-baryonic Fluid), with gravitational (first) density (dark energy) and gravitational waves (at light speed), corresponds to the Gravitation Field of a Cosmological Black Hole (CBH). The latter predicts furthermore a basic emission of Radiation (CBR) from Hubble spherical singular Horizon to the inside of CBH (unlike Hawking’s emission) at an initial singular time. Our solution is then compatible with a well-tempered Big Bang and Expanding Universe (Escher’s Figure, see Penrose, 3) but incompatible with inflation. The latter is based on Hypothesis of a so-called Planck’s particle (Lemaitre’s primitive atom) characterized by a so-called Planck length. We prove that we can short-circuit this unstable particle with a stable cosmological Poincare’s electron with gravific pressure. It is well known that electron is a stranger in usual Minkowskian vacuum (dixit Einstein). The stranger electron can be perfectly integrated in NeoMinkowskian Radiation fluid and then also (with its mass, charge and wavelength) in (second density of) CBR. Everything happens as if the leptonic mass of the electron were induced by our cosmological field. The unexpected cosmological model proposed here is the only one that predicts numerical values of (second) density and temperature of CBR very close to the observed (COBE) values.


Introduction: NeoMinkowskian Gravitational Vacuum as Solution of GR with CC
Let's summarize first how we come to an unexpected Gravitational NeoMinkowskian Expanding Vacuum which "looks like" de Sitter's Expanding Vacuum [1] [2].
( At first glance, these two approaches to Vacuum (0-dSM and 0-MM) are very far apart. We first show (in introduction, see also JMP previous paper) that they are indeed very close (6). 1 The only way to develop the role of CC in NeoMinkowskian Vacuum is to start from that of CC in Riemanian Vacuum.
(2) Cosmological Constant (CC) in Expanding Riemannian Vacuum In cosmological literature we never find (1) but we always find (anti-1) with Riemannian Metric (RM) g µν ( (anti-1) The cosmological term g µν Λ (first member) is associated, by the cosmologists, with the density term (second member) 4 8 G g c µν ρ π . This so-called "component of vacuum" (Dark Energy) is then associate to 0 p ρ + = (next to other components: radiation component, matter component...).
In order to avoid the fateful. We have in our strategy "one and only one equation (0)" with one and only one solution (1 bis, 9,12) 2 .
In order to find the characteristics of Dark Energy, cosmologists develop the thermodynamics underlying the relationship Nothing prevents then introducing a variability over time and therefore a growing energy in an expanding empty universe: which can be developed d 0 V ≠ on the basis of any metric g µν included µν η . This is our starting point (2) with a very binding determination of the metric: g µν µν η = (as we will see it, NeoMinkowskian constraint of inaccessible singular (<c or >c) velocity is very strong). (

3) Cosmological Constant (CC) in Exponential Expanding NeoMinkowskian Vacuum
The first Minkowskian constraint on (2), in a pseudoEuclidean space-time 4D framework, involves a spherical (Euclidean) 3D symmetry: The non-static NeoMinkowskian GMV has to be treated with a radial scale 2 We will see ( 5) that another density that corresponds (see 4) to the same solution.
We have thus a global variable pseudo-mass a ( ) ( ) Nothing prevents a priori that this pseudo-mass from being sensitive to Newton law of gravitation.
On one hand a static model with potential energy P GM E R = − is excluded because unstable (collapse).
On the other hand a dynamical model, based on an equilibrium between kinetics energy c E and potential energy P E , is possible: (YP12 with common numbering in the French and English version of our previous research [1] [2]) 3 . We simplified with a Non-Zero enigmatic Non-Baryonic (NB, That means that our dynamical equation (4,YP12) is an alternative to historical Einstein's determination of constant χ in (0) with weak Newtonian Gra- 3 A dynamic fatal objection seems to be however formulated here at this stage: Our model (YP12, 4) is neither Minkowskian nor NeoMinkowskian because gravitational law with especially kinetics energy would non relativistic. That would be true for a material (baryonic) point ( 3). We urge the reader to be cautious (and patient, 3) because no one has tried until now to apply scalar (temporal) Newton law of gravitation to a space point (we are in the framework of GR) that is to say a non-baryonic (non-material) pseudo-mass. Nobody really knows (at this stage) if this law (4) is incompatible or not with MM. 4 With 0 Λ = we return to static Minkowskian usual solution The determination of constant χ with NeoMinkowskian gravitation field (4) is then much more direct than that with the weak gravitation field.
On the basis of YP12 we rediscover gravitational (critical) density (1-bis) in function of (measurable) Hubble's constant (see numerical value in annex 1 with Gauss cgs-units): Our non-usual solution consists therefore in an Exponential Expanding (EE) of Global Vacuum with a Hubble (measurable) Constant which defines the kinematics underlying the future gravitational dynamics, 1): It was at this point that we had arrived in our previous work [1] [2], (6) in keeping with recent observations of an accelerating (see 10) expanding universe [3].
Nevertheless the originality of our NeoMinkowskian EE of Vacuum, very close to deSitterian EE of Vacuum (with zero density, 1-4), did not seem obvious yet.
So the binding singularity of light velocity, underlying any Minkowskian (or NeoMinkowskian) solution, does not appear in (6). Except if we impose a structural speed of NeoMinkowskian space-time ( ) in Initial Conditions (IC). This is the reason why we suggest to examine first, on a kinematic point of view, the contrast "deSitterian IC ( 1-1) versus NeoMinkowskian IC" ( 1-2).

[TACHYON] Only Can Escape (to the Outside) from Cosmological Horizon of NeoMinkowskian Black Hole
The structure of the paper will follow 3-partition of NeoMinkowskian space-time: Tachyon (v > c) 1, Photon (v = c) 2, Bradyon (v < c) 3.

Undetermined Initial Conditions (IC) in deSitterian EE (Inflation)
Let's take a look at deSitterian solution that consists of canceling the second member: On the left we write Einstein's equation (0) and on the right radial Friedman's equation 5 with Robertson-Walker's metric. The latter is based on two factors (scale factor ( ) a t and curvature factor K). 5 Let us note that NeoMinkowskian solution (1 or 5) is also a solution of Friedman's equation with ( ) 1 a t = ( 0 K = ). The scale factor disappears. Everything seems static. Unless the scale factor is hidden in a scale hyperbola (2)(3). We note that our model does not correspond to pseudo-hyperbolic value of parameter We propose the numbering "anti"-6 for three reasons: 1) deSitterian Hubble constant is not connected with density ( 0 ρ = ) and so to a determined gravitational dynamic (5 bis).
2) deSitterian IC are undetermined, ( ) ( ) , for the radial distance ( ) 0 a and radial velocity ( ) 0 a  as well. We can choose to introduce the radius of the so-called Planck's particle (Planck's length, see annex 1), Poincaré's radius of electron, Bohr's radius of atom, Erathostène's radius of Earth, diameter of solar system, diameter of Milky Way as well.
3) In de Sitter's model (dSV) there is no singular IC (Horizon). It means that the spherical surface (for example the radius of Hubble) ( ) ).

Determined IC in NeoMinkowskian EE: From Singular Velocity to Singular Cosmological Horizon
If we set the light speed ( ) in (6)  The only physical (and logical) consistent interpretation of this double discontinuity (Horizon) involves a singular EMISSION of light, at the (fixed) speed c, from a singular spherical surface Horizon whose Radius ( ) Unlike de Sitter's initial radius, NeoMinkowskian initial radius ( ( ) must be the Horizon of Hubble (binding determination induced by CC).
Unlike usual Minkowskian theory, NeoMinkowskian theory (6)  The paper could then not stop here because we are looking for a full description (kinematic and dynamic) of NeoMinkowskian space-time (tachyon, photon, bradyon).
In order to do that, let us now introduce our Kinematic NeoMinkowskian IC in Dynamic YP12 (5) at singular time With a new gravific dynamic IC we deduce the threshold escape speed: An Horizon from which a PHOTON cannot escape (only Tachyon can es- 6 Since there is neither observed expansion of the galaxies themselves nor the solar (or atomic) system itself, the existence a priori of a Hyperbolic Horizon is then consistent with current observations . cape) is by definition a Schwarzshild's Horizon of a BLACK HOLE.
More precisely: A Cosmological Black Hole (CBH) whose Universal Schwarzshild's Horizon is Hubble's Horizon.
In parallel with a 3-partition of the speed space (tachyons, photons and bradyons), our CBH involves a 3-partition of space itself (out, on and in). THE searched GRAVITATIONAL FIELD GMV which corresponds to gravitational density (1, 1 bis) is given by A UNIVERSAL NEOMINKOWSKIAN BLACK HOLE (CBH).
Underlying Minkowskian Metric MM must be then written as follows: On such grounds it is no longer possible to claim that MM is incompatible with gravitational density (1 bis), with gravitational field in vacuum (8) and then also with possible existence of GRAVITATIONAL WAVES at light velocity. This is exactly Poincaré's position in 1905 with his "Gravific Waves" 7 : "Quelles modifications elle [la transformation de Lorentz] nous obligerait? apporter aux lois de la gravitation. C'est ce que j'ai cherché à déterminer. J'ai été conduit à supposer que la propag ation de la gravitation [ondes gravifique dixit Poincaré] n"est pas instantanée mais qu'elle se fait à la vitesse de la lumière" (introduction) [4]. The only way to make relativistic Laplace's formula (9 with 10) consists in claiming that alone tachyonic points can escape from event Horizon. But we need then a gravitational field (CBH) which does not exist in usual SR. YP-12 involves that the desired GMV is then CBH in NeoMinkowskian global solution (with a negative hyperbolic curvature, see 3).
At this stage our NeoMinkowskian Black Hole (CBH) seems very close to that 7 We purposely used the term GRAVIFIC WAVE used by Poincaré in 1905. Laplace considered that a velocity CAN be super-luminous: "La gravitation se déplace au moins 300 fois plus vite que la lumière. Poincaré criticizes Laplace in 1905 by proposing that the speed of a gravitational wave must be the limit (singular) speed of light on the basis of Lorentz Transformation (LT)". Poincaré's position on gravific waves is non orthodox because SR is reputed without gravitation, without density (1 bis, the putsch note 1) and then without gravific waves, note 8).
He shows also (in 6 of the same paper) that ELECTRON undergoes a GRAVIFIC pressure ( 5-2) in the framework of LT. Thanks to NeoMinkowskian approach, we will be able to synthesize the G-wave and the G-pressure ( 5-2).  So we have to continue our path from very formal and abstract maximal (centripetal) acceleration for tachyon, to a very physical and concrete minimal (centrifugal) acceleration for bradyon (25) 9 . We will show that this hyperbolic acceleration is a universal invariant  and therefore all the above dynamic gravitational equations are perfectly relativistic in NeoMinkowskian meaning.
Finally we check the consistence of our approach with the deduction of the "second" usual cosmological parameter (Hubble H Λ and acceleration q Λ ): In truth they are here both sides of the same coin. Let us insist on the necessity of not confusing 1 q Λ = − with 1 K = − . In the first case it is a reference to a basic global hyperbolic motion ( 1 q Λ = − ) with constant acceleration M α whilst in the second case it is a reference to the pseudo-hyperbolic value of local curvature ( 1 K = − ) parameter in RW metric (note 5).
By conferring a positive role to an essential component (tachyons) of the NeoMinkowskian non-baryonic framework ( 0 G µν = ) the unique solution (1 or 9) can henceforth be written: Supra-luminous speed of tachyon is perfectly allowed in GR for space-points. 8 We have somehow established a theoretical horizon for formulas of flat universe ( 0 K = in RW, see note 5). The problem is that this Horizon must be Hyperbolic (see 3). 9 Outside the CBH (minimal light velocity) we have a minimal H R coupled with a maximal (centripetal) M α . Inside the CBH we will have exactly the opposite (minimal centrifugal M α 3-3).
The objection that the acceleration cannot be a relativistic invariant is inadmissible because both theories are not in competition at this stage. The question will arise when the bradyon that matches to tachyon will be defined. To reassure the reader, we will have (   ).
Is this the only possible density? Is there another density defined by which is not directly the unique solution (1, 12) but which is coupled ( 4 see the ratio anti-32 & 5) with the density (1-bis, 1-ter)?

A Cosmological Hidden Non-Baryonic Micro-Mass?
Both Newton s laws (Gravitation and Dynamic) are coupled ( 0 t = ): (density 1bis can be write We see that we have next to a Macro Force (13) a Newton's law of dynamic a micro force (14): (14) is, at this stage, undetermined (NB micro-mass will be precise in 4). This will be a very important point for Poincaré's "dynamic of electron" ( 5) with a gravitational force ( NB e m m = ?).

From Static Stellar Black Hole (SBH) to Dynamic Cosmological Black Hole (CBH)
Let us show now that CBH, with non-static MM (13) is the cosmological limit of Schwarzschild's static metric (Stellar Black Hole, SBH). The latter is written (Outside the SBH): coupled with formula of Laplace ( ). It is well known that the infinite behavior r ∞  of (schwarz-out), brings back to the usual static Minkowskian This is a happy destiny for Stellar SBH which becomes Universal CBH (9).
It has been showed (Kruskal) that "singularity of Schwarzschild" S R is not a true physical singularity. We have to analyze the essential difference with the singularity (of Horizon) of Hubble H R which is a true physical (hyperbolic) singularity ( 3). The structure of the paper will follow Feinberg's partition of NeoMinkowskian space time: Tachyon

[PHOTON] Emitted to the Inside: From CBH to CBR (Cosmological Background Radiation)
NeoMinkowskian Universal coupling ( ) , H R c involves NECESSARILY a basic emission of waves (with constant velocity c) from the spherical surface of radius H R (at singular initial time 0 t = ). Let us write LikeLight interval: (If there is no emission we have to apply the acceleration to the singular speed (of the photon) which becomes therefore no longer singular) In what sense of radial direction should this radiation be emitted? To the outside or to the Inside of CBH?
Given that only tachyons can escape to the outside ( 1), the photons ( 2) can only be emitted TO THE INSIDE from the border H R and then in the bradyonic universe.
This is logically unstoppable. Unless we invoke quantum fluctuations (Hawking 1974) in order to justify an emission of Black Radiation to the outside from event horizon of SBH ( 2-1).

Our basic emission of light resembles that of Hawking but it is not that of
Hawking. Except on one point: the emitted radiation MUST be a Black Radiation. Indeed we have an emission of radiation from a global spherical surface of last diffusion, based on an isentropic transformation (2 & 40).
Our CBH is consistent with a singularity of the type Big Bang coupled with an emission of the type of CBR (Cosmological Black (Background) Radiation (a CBR at the Horizon of the CBH?). We will show in the next paragraph that is also compatible with an expansion of the type Hubble ( H R is an Hyperbolic We focus attention on a very important point that (Mink-on, 16) defines a NeoMinkowskian STRUCTURAL space-time velocity (von Ignatowski): it can correspond to light wave (photon) or gravific wave (graviton) as well (see Table 1).

From Hawking's (Local) Black Radiation to (Global) CBR Black Radiation
Let us remember that Hawking's black radiation [7]. is emitted from Horizon of Events of SBH to the outside (see also Unruh, [8]). The expression "singularity of Schwarzschild" is henceforth outdated (still used in the old scientific literature). We confirm this point by making We are indeed getting a non singular speed as large as we wish for SBH. But a speed of what? It is not speed of light c. Given that we are in the framework of GR, this supra-luminous speed can only be that of space point and therefore to the speed of propagation of gravitation (see Laplace, note 8).

R c with singular Horizon of light velocity c (Zero interval, or
LightLike interval, see Table 1, we repeat 16-on, just above): Our Black Hole emits not only CBR (see Table 1) but also gravific waves at the speed of light (Poincaré, 1905, [4]) to the inside.
Inside the SBH we have: (1 ter) In the last case it's as if our universe
If it is almost impossible for an observer to get into a usual SBH, it is radically impossible for a (bradyonic) observer to get out of a CBH.
Fortunately the interior of CBH is precisely the Universe or the World itself. Fortunately also the observer is in the right place to measure the CBR emission (see abstract).
This the reason why we suggest going beyond the notion the notion of " Hole" and replace it with that of the "W(hole) World" or "The Black Whole Universe" given that it is filled with Cosmological black radiation of the kind CBR (emitted from Horizon of Hubble of CBH (in 0 t = ).

Cosmological NeoMinkowskian Scale Hyperbolas and Perfect Cosmological Principle
Given that cosmological kinematics is radial ( r x = ) we can reduce space-time at We rediscover the 3-partition with singular asymptote (c = 1): a point on this asymptote can be photonic or gravitonic as well [4]. We can transform the coordinates of a point-graviton with LT into another point-graviton on asymptote (with zero interval). We must now focus on bradyonic hyperbole (18. It must now be shown that Hyperbole (18) is the global (intergrated) form of local (differential) metric: Table 1). (The structure of the paper will follow Feinberg's 3-partition of NeoMinkowskian space time: Tachyon 1, Photon-Graviton 2, Bradyon 3)

[BRADYON] Galaxies That Are Approaching a Hyperbolic Horizon (Escher Figures)
Let the tachyons go (We caught the comet by the tail!) and install us in the inside of CBH (in the Black Universe) in order to complete NeoMinkowskian pace-time with non-baryonic ( 0 G µν = ) bradyons ("as long as we have not everything, we have nothing"). The Whole Hole is the Whole Universe if we can express ourselves in this way.

Boundary Conditions for Bradyons, Law of Hubble and Double Special Relativity (THESIS DSR)
In Inside the CBH the (radial) law of Hubble, coupling "large velocity-large distance ( r x = )", must therefore govern the expanding of galactic space points of the cosmological fluid (at a fixed time): v c H r This CONDITION OF RADIALITY 11 (coupling "large velocity-inter-galactic distance") is quite basic. There is no expansion for "short" (non-large) distance and then for Planck's length.
The problem is now that it is difficult to see how a MM (see Table 1 2 , Mink-in) could be at the basis of such expanding kinematics (this is our THESIS).
Remember that so far there is only one solution (12)

Accelerated Motion of Material Point and Lobachevskian Velocity Space (HYPOTHESIS SR)
Pauli remarks that the Worldline of usual (standard) relativistic Uniformly Accelerated Rectilinear Motion UARM in SR coincide with usual scale hyperbola (along Ox, 18). Indeed we have the following hyperbolic worldline UARM (Minkowski 1908) in inertial system K ( 0 from which Minkowski deduced in 1908 by a double integration (18 bis). Minkowski's proper time of accelerated particle interests us particularly because it is directly connected with ( ) This is the basic concept of Radial: Expansion only applies on a very large scale (distance and velocity). In fact this paper is devoted to translations (dark energy). The next will be devoted to rotation (dark matter, see conclusion). The one-third factor 1 3 ) are there to remind us that we are in space 3D (see also initial ratio, 2 bis, electron and density-pressure for EM radiation 5).
And then a hyperbolic sinus written with hyperbolic (index h for hyperbolic) velocity h w c ατ = 12 : Using for hyperbola (anti-18) the hyperbolic polar coordinates ( ) we deduce by differentiation (we refer 18 for Hyperboles, 19 for inequalities, 20 for metric): ( ) which corresponds to proper time (20) and "looks like" to Mink-in signature We specify that 20-MM is not a true MM because either " h w is variable with This is the reason why Rindler () introduces a NON-MM for his cosmological model based on (UARM): Let us now return to the motion of accelerated material point and focus on his hyperbolic velocity which is defined by the inverse hyperbolic tangent (see 21) We have then a centrifugal proper acceleration which is derivative, with respect to proper time, of hyperbolic velocity: 12 Or Rapidity of Robb: 1 2 w w w + = . 13 Rindler introduces, on the same basis (UARM) induces also a Black Hole but not a CBH. Let us now take a look to the geometry underlying UARM.
It is well known that in pseudoEuclidean SR, the space itself is Euclidean whilst the "space of velocity" is non-Euclidean, in Lobachevskian meaning (relativistic addition of velocities) More precisely according to Borel [9] global "space of speed" is characterized by a negative curvature  We underline that in usual SR the velocity space is a true complete Hyperbolic space (with distance introducing by cross ratio) in strong sense of the term non-Euclidean (Penrose [11]). This is not the case of the pseudo-hyperbolic spaces defined in Friedman's equation with 1 K = − (where scale factor is given by a sinh (20) and not a tanh (24) which defines a Non-Euclidean Distance (24) (see 3-3-2) (Note in 21 bis that the time and the space are respectively given by a sinh and a cosh).

DEMONSTRATION: From SR without Gravitation to Gravitational DSR
The demonstration must be done in three stages (Gravitation and Geometry): 1) Hubble constant with its corresponding global Gravitation field ( 3-3-1).

NeoEinsteinian Principle of GLOBAL Equivalence between Gravitational Field and Minimal Acceleration
Let us introduce now NeoMinkowskian singular bradyonic hyperbole (18) This MM (17-in) corresponds to a global gravitation field. 14 (G-DSR) with Hubble Horizon: The answer to first Pauli's question ("To which global gravitational field in GR does this UARM corresponds 15 ? [13])" is then (23) and therefore (33). We answer with a global (cosmological) NeoEinsteinian principle of equivalence Part one of the thesis ( 3-3-1) is thus demonstrated: we have Hubble constant but we do not yet have Hubble law itself (19bis) ( 3-3-2). We are at this stage close (except Planck's mass) to cosmology of flat Universe [5].

CC Induces in G-DSR a Global Negative Lobachevskian
Curvature of Space (Escher) Until now our NeoMinkowskian Universe seems to be a Flat Universe, in the meaning of Tatum [5] because LOCAL Einsteinian curvature tensor is zero ( 0 G µν = ). There is no contradiction because we will prove now that there is a GLOBAL curvature for Euclidean 3D space (Penrose).
After the G of Gravitation let us now deal the G of Geometry. What about the geometry of space 3D itself in G-DSR?
Let us apply formula of Cayley-Klein's hyperbolic distance (24), respectively with ( , h s r and H R ), which can be considered here as the singular RADIUS OF 14 We thus ended the forced cancellation of the gravitational NeoMinkowskian density (the putsch, note 1). We follow the same path as Unruh ([8]: Behind Hawking's local radiation there is a kinematic of uniform HYPERBOLIC acceleration. We transform therefore Unruh "local" effects into global (cosmological) effects (we change also the sense-and the meaning-of the emission). 15 Historically Pauli did not find this field because he was using the GR WITHOUT CC!  THIS IS AN EXTRAORDINARY RESULT: In G-DSR it is not only the "velocity space" (22 bis) but the "space itself" (25) that is Lobachevskian. We obtain a whole (Global) Lobatchevskian "distance" (a scale factor) with hyperbolic function of tanh (22 and 24) and not a scale factor defined with sinh (21 bis and Friedman's model with 1 K = − (see Penrose [11]). There is no contradiction between the cancellation of the local curvature factor 0 K = in RW metric (note 5).
Beltrami's abstract disc is concretized by famous aesthetic hyperbolic Escher's disc. The fact that the W(hole) Universe (with our observer) is inside a CBH is not tragic because first we are enlightened by CBR and then we fit in a harmonious (in Penrose's meaning) hyperbolic figure (disc) of Escher (Cayley-Klein' s hyperbolic distance). Hyperbolic Universe is then compatible with radial expanding (without end) of galaxies and with Perfect Cosmological Principle (a horizon of finite space is aligned on a horizon of finite time).
While the tachyons move away as they escape (without end) from gravitational field (25) the galaxies move away infinitely (hyperbolic velocity) as they approach (without end) the (hyperbolic) horizon ( 3-3-2) according to the law of Hubble (19-19 bis).
Milgrom's minimal acceleration [14] or Hubble's constant are then effects of hyperbolic (negative) curvature of space 3D.
By taking into account the CC (Einstein 1917) in GR (Einstein 1915) and therefore a minimal acceleration M α in equation of geodesic (Einstein 1915): Exactly as in the flat universe [5], Christoffel

Hyperbolic Tangent versus Hyperbolic Sinus:
The "Big Bang", An Effect of (Negative) Curvature? We have to apply the same hyperbolic definition (24) which is internal EE corresponding to basic external EE YP12 (4), (6-6 bis). 16 Pauli was intrigued by the notion of proper acceleration in proper system K' which follows the fluid (medium) at rest in K (in SR): In relativistic kinematics we will naturally describe by as "uniformly accelerated" a motion for which in a system K' moving with the medium or particle is always of the same magnitude α . The system K' is a different one at each instant; for one and the same Galilean system K the acceleration of such a motion is not constant in time [13]. In SR "The system K' is a different one at each instant" (successive K-K' Lorentz boost). Pauli considers then a single global (hole) system K' is a non-Galilean system and moves therefore to GR ( The "fatal" objection of the note 3 is therefore refuted: Our basic equation YP12(4) is perfectly relativistic (in GR and in DSR meaning as well 17 ).
In G-DSR Doppler Galactic Redshift formula We notice a quadruple contrast.
In contrast with radial Doppler formula in SR the velocity β is the velocity of a space-point.
In contract with the other Redshift z formulas in GR, velocity β is strictly infra-luminous (<1). In contrast with de Sitter, where there is not singular velocity for space-points) in G-DSR there is a double singular velocity for light wave (Photon) and for gravific wave (Graviton), as well.
In contrast with de Sitter, the expanding (29) G-DSR is only valid for large distances coupled with large velocities 18 .

Intermediate Conclusions: Lepton Electron Is Not a Baryon
Our NeoMinkowskian non-baryonic solution of GR with CC defines a Universe characterized by a (very large) finite Hyperbolic Hubble Horizon H R at its (singular) origin. Hyperbolic Universe is incompatible with inflation but compatible with the most undeniable observations: Galactic expansion and emission of non-galactic black radiation (CBR) a (very long) finite time H R ago. 17 Among the two speeds ( ) Until now NeoMinkowskian model is without non-baryonic light emitter. Without the missing link, Poincaré's gravific electron (pressure of ether, 5), we cannot, at this stage make, any numerical evaluation or prediction.

A (Stable) "Cosmological" Electron to Short Circuit the (Unstable) Primitive Atom?
Let's test the candidate electron [16]  Pauli's answer (p 93): "Hyperbolic motion thus constitutes a special case for which there is no formation of a wave zone nor any corresponding radiation".
Pauli find a ZERO magnetic field (and then no radiation 19 ) and hastens to specify that locally (parabolic) the electron emitted a radiation (see note 16 and also numerical annex).
In NeoMinkowskian limit of GR with CC, we can suspect a link between this 19 Einstein's Boost is based in SR on infinitely slow acceleration ( Our future integrated (stable) electron is the ideal candidate to Short-Circuit (unstable) Planck's particle (Lemaître's primitive atom)?
Reset then by using following writing of MM:

The First and the Second Density
This enigmatic force G f of synthesis will have to be placed, next to How can we justify the entry into scene of electron with this second density (pressure) in our NeoMinkowskian Universe? At the beginning of 3 we claimed that "we caught the comet (devil) by the tail (tachyons)". We have now reached the head with bradyons: We draw attention to the fact that there is "tachyonic" FIRST density (dark energy) but until now no "bradyonic" (electro-photonic) SECOND density (see

The Second Density: From Electronic Density to Density of Gravific Waves
Cosmologists distinguish three different types of Fluid which corresponds to three periods of the universe: 1) the dust or inconsistent matter ( 0 p = ), 2) the dark energy 0 p ρ + = (anti-1) and 3) the so-called "Radiation" 1 3 em em p w = (35) (generally reported, in cosmological literature to a "radiative period of Universe") 20 .
In cosmological literature the fluid (37) is always called "Fluid of Radiation" (always written in Riemannian metric g µν ).

Hidden Electron and Hidden Graviton in NeoMinkowskian Perfect Fluid "Radiation"
We absolutely need to introduce the light (emission of CBR in 0 t = ) in Neo-Minkowskian Fluid: It is generally claimed that, if we replace g µν µν η = in (34) from a Riemanian Fluid to a NeoMinkowskian Fluid the gravitation (and then gravific waves) would be eliminated (see the putsch note 1). It is obviously wrong because NeoMinkowskian limit imposes only a LIGHTLIKE 4-vector. The latter can correspond to a photon or could correspond to a (hypothetical) graviton (like light) as well.
In other words, for a classical light wave or a (hypothetical) "classical gravific wave" as well: (a being dimensionally an ACTION). We are therefore perfectly entitled to write next to "Radiation" Fluid (35) a "Gravitation" Fluid (36): The relationship (36) GW T µν in MM (33) is much more restrictive than it seemed at first glance.
We will prove that Poincaré's GW not only COULD exist but that they MUST exist (determined action a and Ge λ ).
The difficulty being here more logical than mathematical, we resume the situation with the following Table 2 (tachyons are gone):

Hidden Electron in (Cosmological) Fluid "Radiation"
For the first time we take now explicitly in consideration TIMELIKE 4-vectorial writing for velocities in the so called Radiation fluid (38).
Let us try to transpose the notations of the previous Given that it is impossible to put directly the velocity of light c in such a timelike 4-vector, the radical singularity of our basic border " v c = " is then structurally inscribed in temporal component 0 u c = for an "electronic point" (at rest) There is then a hidden electron in Cosmological tensor of "Radiation" (a cosmological electron?). Let us see this crucial point in details: 1) The first tensor (left member) is usual EM tensor of radiation with null . This is the reason why the perfect fluid (38) is called "Radiation" in cosmological literature.
2) The second tensor looks like that of an "electron" at rest 1 0 u = which would hide behind its density (see Poincaré,. 3) The third tensor (of pressure) with timelike MM is exactly the one we were looking (33) in Gravitational G-DSR ( 3-3, 23-G and 33) with a (possible) way to the determination of the missing coefficient (or the second density).
This triple statement is not very original because it corresponds exactly to that of Poincaré in 1905 ("La dynamique de l'électron", 5-2). So far we have, at this stage an abstract electronic point but not yet a concrete electron ( ) , , e e e m r .
Let us remark that we can put in (35 or 37) the pressure to the left:  This analysis shows that in "Radiation" tensor of Cosmologists there is not only a hidden electron but also a connection of this electron with gravific waves.

Hidden Electron in (Cosmological) Black Radiation
The concrete radiation in our cosmological problematic is black radiation in CBR. Let us remark, in this respect, that the situation of concrete electron Let us finally note that according cosmological usual "Isentropic Expansion of Spherical CBR" (see basic Equation (1)-anti(1)):

Synthesis between Poincaré's Gravific Electron and Poincaré's Gravific Waves
We have to find a new synthesis for our Trio: ELECTRON-PHOTON 21 Given that non-baryonic ( 0 G µν = ) Redshift is based on light emission by galactic... baryons, we are missing non-baryonic emitters. Leptonic electron (a renowned emitter!) could be a good candidate 3-6 and 4).
(L-Wave)-GRAVITON (G-Wave). In order to do that we need to start a concrete electron ( ) , , e e e m r .

Poincaré's Historical Induction of the Mass of Electron with Gravific Pressure
In 1905 in his basic paper on "La Dynamique de l'Electron, Poincaré is looking for a determination of mass e m electron from its EM emitted field (July, 6 Lorentz' Contraction, see note 20). He discovers that a purely EM induction of the mass is not possible because we have to take into account a strange Non-EM pressure (probably) of gravitational origin [4].
From Energy-Impusion tensor EM T µν Poincaré notes (with LT) that energy and impulsion of a purely EM Electron are not transformed ( Poincaré then adds to the EM tensor a Non-EM tensor in such a way that these parasitic thirds are eliminated (41). Mathematically it means that the diagonal terms of new tensor ( Poincaré does not write in 1905 any formula for its internal density (or pressure) but specifies (in the sentence where he claims gravitational origin) that the density is proportional to the "fourth power of experimental mass e m of elec-22 Such a name "classical radius of electron" is inappropriate in Poincaré's theory because he designates his electron as a "Hole in the ether". In modern language this is similar to that of quantum theory of field (QED of Dirac-Feynman): Poincaré's electron would be "singularity in the field". From which cosmological field the mass of electron is inducted? We are waiting for the answer from QED. We have a WED answer ( 5-6). According to Poincaré the main physical argument for the gravitational origin of his pressure is that it must be attractive (anti-electrostatic). With the same argument being that, in a rather enigmatic way, that his gravific pressure must be negative (nothing to do here with

Poincaré's Negative Pressure and NeoMinkowskian Perfect Fluid
M (The first is classical EM with zero trace). Poincaré's mathematical answer would be logically: This is exactly the perfect fluid (39) with an electron at rest ( 5-1).

EM_RADIATION + GRAVIFIC NEGATIVE PRESSURE-
and therefore the pressure is no longer negative! Poincaré's negative gravific pressure becomes in NeoMinkowskian Fluid a positive pressure with MM (see 37bis and 37ter).
Nothing prevents then to affirm (dixit Born) that everything returns in a purely EM order with The situation seems hopeless so we must ask questions (we propose the three following questions).

Did Poincaré (Langevin) Choose the Right Density?
Did Poincaré (Langevin) choose the right density? In other words: Is the coefficient (density e w ) considered the right one in (33)?
The missing link (see 33) density of the anti-electrostatic force is very huge 10 8 g/cm 3 (stability of elementar electron) and not very credible in the role of density of radiation, Reported to black radiation of CBR this first attempt involves e CBR w w = (see 40, the density involves a temperature) we obtain about 10 15 K! At this stage we have not discovered yet the missing coefficient. Moreover Langevin-Poincaré's density (35-10) is connected with gravitational theory but the constant G is hidden (in 48).
Constant G is however NOT hidden in the third formula of gravific density.
Remember ( 4) that there are three densities that we can report (logically) to Feinberg's trio (tachyon, electron, photon (+graviton): 1) The first tachyonic density is the density of dark Energy (CC).
3) The third enigmatic (Ge) Gravifico-electronic (very tiny) density (40) with very weak gravitational long range force (in contrast with the first, huge gravitational long range force).
The ratio This third density could be reported (logically) to Photon or Graviton, Radiation or Gravitation. The question is: a density of what? (this is not a density of mass in electron, see 44).
It can only be a density of light waves or density of gravific waves. " E Pc = " for electron (with non zero proper mass) and photon (with zero proper mass) as well! In other words, can an electron moving at the speed of light turn into ... photon? No! Ask the (almost) same question but otherwise.

Does the "Perfect Ultra-Relativistic Electron" ("PURE") Exist?
For photonic gas we have rigorous relationship That is to say: Does the "PURE" exist? If limit electron ( v c = ) or Cosmological Electron does not exist, then the primitive atom exists. All the above is based on (35 and 35 bis) 23 . So let's forget for a few moments (35) and let's take a look on (36 and 36 bis).
Remember that Poincaré never establishes any direct link between his GRAVIFIC waves (introduction) and his GRAVIFIC pressure on electron ( 6) [4]).

From ELECTRON TO GRAVITON: Synthesis towards (Second) Density of Gravific Waves
Let's reverse the reasoning from (36) that defines the Graviton (or Gravific Wave) by assuming that there is (maybe) a link with "PUR" electron (Ge).
If PURE exists then it defines a Gravific wave (lightlike Graviton, SEE previous Frequency Ge ν will be connected with angular velocity of Thomas 2 T Ge ω ν = π see conclusions 25 .
The limit electron does not give a photon but a graviton 26 .
The lightlike graviton is without proper mass. The mass of electron is in fact carried by the G-wave in (51). We suggest calling this mass e m (without proper mass 0 G µν = ) a "comobile mass" of graviton (without charge 27 ) exactly like galactic fluid (see also comobile time, [3][4][5].
In NeoMinkowskian G-DSR the "Wonder" namic (WED) ( 5) should preside over the destiny of Quantum Mechanics or Quantum ElectroDynamic (QED). We know a little more today with NeoMinkovskian CONTINUUM which adds a decisive gravitational component (G-WED) to de Broglie's subquantum substratum [16]. The unified field (G-DSR is a G-WED) is photonico-electro-gravific (

5-4).
We suggest here to continue with relativistic mind of de Broglie. The only difference is that we use both SR and GR (and therefore G-WED) in order to determine (we put in evidence sub-hypo) the SUB (microphysics quantum stratum).
The most fundamental principle of QED (microphysics) is that the LEAST action corresponds to h (or  ). In G-WED (Hypomicrophysics) we have the following LEAST action (52): , in harmony with continuous spectrum of CBR, is smaller (SUB) than the " quantum" of action. The fine structure constant becomes then a decisive factor between G-WED and QED in its two forms (Sommerfeld or Planck Einstein): With Stefan-Boltzman's formula (39, 40 and 80) and numerical annex 1) we

Conclusions: From Cosmological Electron to Galactical Electron?
Rather than the Quantization of GR (main stream) we chose here the GR-ization of Quantum (electron). The NeoMinkowskian synthesis between Poincaré's GRAVIFIC waves and Poincaré's GRAVIFIC pressure on electron is now complete.
Planck's unstable cosmological particle is then shorted (short-circuited) by stable cosmological electron which is in fact the graviton.
Hyperbolic NeoMinkowskian Universe not only predicts a CBR but also the Temperature observed of this CBR.
We follow Penrose [18] on two essential points: 1) "There is something particularly elegant about hyperbolic geometry". G-DSR (introduction and 1-2-3) 2) "I should say that I do not really believe these (inflationary) theories".

G-DSR ( 4 intermediate conclusions and 5 conclusions)
The most beautiful result of Lobatchevskian interpretation of "Big Bang" or "Big Boost" may be: The finite time H T is an effect of the curvature of hyperbolic straight line of time ( 3-3-3, 27).
Cosmology joins geology: catastrophism or inflationism (with a Big exceptional Bang of primitive atom) against unifomitarism or gradualism (with Big Well tempered Boost).
We are aware of the incompleteness of this present exploration. In our approach everything seems RADIAL: there is no RADIAN (no aberration). We have a cosmological electron (Translation) but not a galactical electron (Rotation).
Nothing is circular (UCM), everything seems rectilinear (UARM). Everything is longitudinal, nothing is transversal: the magnetism seems gone (der verdammte magnetismus, sagte der junge Albert zu Mileva). It could come back in force transversely.
An alternative to the escape velocity (Dark Energy) of this paper however exists: the orbiting velocity (Dark Matter). The only difference is given by a factor 1/2 (in YP12).
The composition of two LT not in the same direction involves Thomas' Rotation (angular velocity connected with frequency of wave electron, 52). According to Pauli's, Thomas' rotation is a decisive correction of factor 1/2 in Dirac' spin 1/2 of electron.
(Remember also that all this was done in the absence of baryons ( 0 G µν = ) and also especially in the absence of neutrinos).

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.

Numerical Annex 1: From Cosmological Electron
to Gravific Density of CBR

Some Cosmological Constants and Poincaré's Cosmological Electron
Critic density of tachyonic dark energy from Hubble's constant (1 bis): ( ) Or the usual inverse ratio: we find an absolute temperature of (57).
Observed CBR (COBE) values: and invariance (limit) of light velocity but they are singularities that seemed ir- Einstein's LichtKomplex were considered as horrors (or terrors) by Lorentz, and Planck (and most of physicists). LichtKomplex were rejected by the community of physicists because they presuppose that a certain amount of matter travels at the speed of light. Einstein eliminated them in all subsequent presentations of his SR (already in 1907 ...). Their radical elimination will persist even after 1922. They were ejected from both History of Physics and Physics itself. Why?
Both they use LT of a spherical volume but Poincaré considers ( 1905 1 Einstein deduces the existence of spherical particles "whose energy transforms proportionally the frequency". The coefficient of proportionality is then not  but 2 e c (see 52).
Thanks to GR (Einstein 1915) with CC (Einstein 1917) with Poincaré's (Neo-Minkowskian) Limit, we now know that when (the young) Einstein makes : v c = (reSIC) in Poincaré's electron, he determines not a photon but a graviton (see 52). The history of physics is highly nonlinear.

Poincaré's Velocity with Respect to the Gravific Ether (Conjecture 2)
The fine structure (without quotes) constant is thus hidden in the synthesis between the two SR (a "Double" SR). called by Einstein "factor 900": 30 Electron, atom, solar system, galaxy are not in expansion. Poincaré could seem "inflationist" at this respect, "Mon lit est en expansion ...". Et il précise "mais je ne peux pas m'en apercevoir"! Le principe einsteinien (quantique) de l'identité des unités de mesure (des atomes) est à cet égard plus clair. Le fait est que Poincaré avait une théorie de l'expansion (ellipsoédes lumineux allongés, note 18) en 1907 basée sur ... la contraction de Lorentz (20 ans avant l'univers de Hubble. With Poincaré's [21] (relative) speed with respect to the gravific ether: 31 (CBR), we have the right to formulate a second conjecture (conjecture of "Big Boost"): If we were at rest with respect to the ether, the "quantum" h and the "continuum" 2 e c would be thus reconciled. 31 Einstein had suppressed in his SR (1905) the ether (with the possibility of measuring a speed with respect to it). Poincaré did not remove the ether because it was a (gravitational) source of the mass of the electron. Note that Einstein reset an ether in 1922 (see L. Kostro) but he could not make the connection with CBR discovered (1965) after his death (1955).