Some complements to my paper posted on ArXiv (1507.00460)

1. Dark matter + energy as Mach’s ether
in LCDM cosmology
Gilles Cohen-Tannoudji
Laboratoire de recherche sur les sciences de la Matière
(LARSIM CEA-Saclay)

2. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 2
Courbure de l’espace-temps Constante
cosmologique
Tenseur énergie de la
matière
La matière dicte à l’espace-temps comment il doit se
courber: l’espace temps dicte à la matière comment elle doit
se mouvoir
L’inconnue: le champ de
métrique de l’espace-tempsL’équation d’Einstein
Constante de
proportionnalité:
1
( ) ( ) ( ) ( )
2
R x g x R g x T x     L  
2
/G c

3. 1
8
2
The Friedman-Lemaître equations of motion
The Einstein equation
Ng G T g      L
 
Matter content of the universe, perfect fluid
T pg p u u      
 
2
2
2
8
3 3
4
3
3 3
Friedman-Lemaître equations
(1)NGR k
H
R R
R G
p
R
 


  L
    
 
L
  
 
; 0
3
Energy conservation, via T
H p


 

  
25/11/2015 DM+DE as Mach's ether vs LambdaCDM 3

4.  
 
2
2 2
2
0
3
8
/
/ 1
/ 1
tot
tot
M R V
Definition of cosmological parameters
c
N
c
H
G
k R H
k R


 

 
  
      
0
1
M b DM
tot b R DM DE
In CDM
k
L

    
         
25/11/2015 DM+DE as Mach's ether vs LambdaCDM 4

5. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 5
Eq. (19.8) has a simple classical mechanical analog if we neglect (for the moment) the
cosmological term L. By interpreting −k/R2 Newtonianly as a ‘total energy’, then we
see that the evolution of the Universe is governed by a competition between the
potential energy, 8πGNρ/3, and the kinetic term . 
2
/R R
Big bang cosmology,
K. Nakamura et al. (PDG), JP G 37 0750021 (2010)
Vanishing of spatial curvature = vanishing of “total energy”

6. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 6
 
2
3
1
/ GR
DE Ether
QFT
DM Ether
QFT GR
Ether Vac Ether Ether
Matter B R
Tot Matter
Ether DM DE
Ether Vac
Our proposal
HL   
  
      
    
     
    
  

L
Dark Matter, Mach’s ether and the QCDvacuum
ArXiv: 1507.00460

7. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 7
Scale factorPrimeval inflation Expansion Late inflation1
A B
C
D
E
LL
Linf
a w
10-60
LP
Past event horizon
Future event horizon
Big-Bang ignition
Today
From radiation to matter dominance
Color confinement
LCDM cosmological SM
HEP standard model
BSM physics
F
EW symmetry breaking
G
Hubble radius L=H-1

8. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 8
• « D'où l'on peut voir qu'il y autant de
différence entre le néant et l'espace vide, que
de l'espace vide au corps matériel ; et
qu'ainsi l'espace vide tient le milieu entre le
matière et le néant. C'est pourquoi la
maxime d'Aristote dont vous parlez, "que les
non-êtres ne sont point différents", s'entend
du véritable néant, et non pas de l'espace
vide. » Réponse de Blaise Pascal au très
révérend père Noël, recteur de la Société de
Jésus, à Paris, 29 octobre 1647 Pascal, Œuvres
complètes, La Pléiade, p 384, ed. 1998

9. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 9
At color confinement scale (Q2 ≈ 1Gev2)
     
0
( )
8
0
DE
Ether Vac QCD
Eff
Zero pointQCD
Vac
Matter DM
Zero point
Matter Vac Vac
D
D D D
c
N
c
G
 

  
  
 
  
L
 
 
  

10. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 10
Baryonic to dark matter energy density ratio and
the quark-gluon parton model
Scaling observed in deep inelastic lepton-nucleon scattering at the confinement scale (about 1.5
GeV2 ) leads to the parton distribution functions used as input in the standard model:
• Three valence “constituent quarks” (with a mass about 1/3 of the nucleon mass) carrying about
15% of the momentum of the nucleon
• “Sea” quark anti-quark pairs and gluons ( that is the QCD vacuum) carrying the remaining 85%
of the momentum of the nucleon
Once confined, the valence quarks give rise of the baryonic matter and the QCD vacuum gives rise
to the dark matter
Quod erat demonstrandum!

11. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 11
The Mach-Einstein doctrine, which has come to be known as Mach’s principle, holds that the basic
inertial frame is defined by distant bodies (Mach’s fixed stars in the original formulation, now to be
understood as the galaxies). According to this view, all inertial effects arise as a consequence of
accelerations relative to the system of distant galaxies. In particular, inertia of matter is due entirely
to the mutual action of matter. It has been suggested by Einstein that such a mutual action arises
from gravitational forces. Then, inertial forces on a body would reduce to gravitational forces exerted
by galaxies when the body and the galaxies are in relative accelerated motion. Since, according to
this point of view, the need for distinguishing between inertial and gravitational forces disappears,
the weaker principle of equivalence follows from the stronger Mach-Einstein principle.
Reformulation of General Relativity in
Accordance with Mach’s Principle
Feza Gürsey Annals of Physics 24, 211-242 (1973)

12. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 12
It also appears that the function f shows up as an inertial coefficient in the equation of motion. This
is directly relevant to Mach’s principle as f, not being a true scalar, will change when masses in the
universe are redistributed by a coordinate transformation. Thus, the inertia of a test particle will
depend on the cosmological structure. It is shown later in the paper that in virtue of our boundary
conditions, the inertial mass of a particle in an otherwise empty universe vanishes.
Section IV is devoted to the study of the properties of a special cosmological background uniform
in space and time in agreement with the Perfect Cosmological Principle. This is known to be a de
Sitter Universe. It is a special conformally flat universe with metric of the form ( 1.1) with lf, f
being a definite function of the Lorentz invariant length. It is shown that, although the de Sitter
universe cannot contain stable matter, it may be interpreted as being associate with a uniform
distribution of mass scintillations, that is, unstable masses that give rise to a singularity in
the equation determining the metric. In the case of a spatially closed de Sitter world a total mass
may then be defined. The metric is expressed in terms of the radius of curvature and the total
mass in that case, all the mass coming from mass scintillations.
 4
( )x

13. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 13
Finally, an important problem that arises from our discussion concerns the stability and uniqueness of
the cosmological structure. We have assumed the universe to have a de Sitter geometry in the first
approximation. This corresponds, as we have seen, to a background of uniformly spread mass
scintillations which could be interpreted as virtual pairs of massive particles in a quantum field
theoretical picture. In the second approximation, taking the average contribution of uniformly
distributed stable matter into account, we may regard the overall geometry of the universe as
conformally flat. Repulsive forces between stable bodies are introduced at this stage. In the third
approximation we also allow for the deviations of the Riemannian geometry from the conformally flat
structure and thus introduce attractive gravitational forces which are superimposed on an expanding
universe. This leads us to question the validity of these successive approximations to the geometry of
space-time. Now, in a conformally flat universe we have found the relation (9.6) in which, according to
(6.13), part of the total mass M’, namely, N comes from stable matter and another part M(0) from the
mass scintillations of the de Sitter background. If our approximation is a good one, we must have
(0)M N
According to McVittie’s (39) discussion of recent cosmological data, if we take as M’
the stable mass in the universe (M(0)=0), then the equation (9.6) is off by a factor of
about 30. This suggests that
/ (0) 3%N M 

14. A new cosmological paradigm
• A non static (“running”) Einstein’s universe, in which the
“running” cosmological constant exactly compensates, at all
epochs the effect of gravity
• The equilibrium thus obtained would be unstable in a static
universe
• But in an expanding universe, such an equilibrium is perfectly
admissible, because it is dynamical
• Rather that “running”, the Einstein’s universe should be said
“biking”
25/11/2015 DM+DE as Mach's ether vs LambdaCDM 14

15. 25/11/2015 DM+DE as Mach's ether vs LambdaCDM 15