Post on 09-Feb-2022
Observational constraints of a matter-antimatter
symmetric Milne Universe
Aurélien Benoit-LévyRencontres de Moriond
March 2008
Rencontres de Moriond 2008
Introduction
The composition of the Universe according to concordance model is rather surprising: 95% is unknown!
Three components successively predominant and then completely negligible.
Before accepting such a strange Universe, necessity to consider the possibility of simpler alternatives
The Symmetric Milne Universe: a flat spacetime with no Dark Matter and no Dark Energy
Presentation and motivations
Confrontation to Type Ia SN, BBN, and CMB
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Presentation of Milne Universe
The Symmetric Milne Universe
A coasting Universe, with linear scale factor, could be an interesting alternative to a strong deceleration at early times and then a phase of exponential expansion. This Universe has a slower evolution at high temperature. Spends about 108 times more time at QGP transition.
Universe very homogeneous above QGP transition. Separation of matter and antimatter during phase transition that creates domains is possible with such a long time available (cf Omnes 70’s)
Equal quantities of matter and antimatter. Antimatter has negative active gravitational mass
Without Dark Energy or Dark Matter
Ωb ≈ 0.3
(a
a
)2
= H20
(ΩM a−3 + ΩRa−4 + Ωka
−2 + ΩΛ)
(a
a
)2
= H20
[ΩM
(a0
a
)3+ ΩR
(a0
a
)4+ Ωk
(a0
a
)2+ ΩΛ
]
(a
a
)2
= H20
(a0
a
)2⇒ a(t) ∝ t
Ωr = 0
ΩM = 0
(= m)
t0 =1
H0= 13, 9× 109 H0 = 70
a(t) ∝ t
η =nb
nγ
p↔ n
× × × ×•Ci−1 Ci Ci+1m
!"d1 !" d2
Ci Ci+1 Ci Ci+1
M(Ci−1) = 0, M(Ci) = m`1− d1
dx
´, M(Ci+1) = m
`1− d2
dx
´
dx
Gravitationally empty Universe at large scales, no acceleration and no decelaration. Scale factor evolves linearly with time:
an in FRW metric implies flat space-time and open space. Compared to usual assumption of flat space.
Ωb ≈ 0.3
(a
a
)2
= H20
(ΩM a−3 + ΩRa−4 + Ωka
−2 + ΩΛ)
(a
a
)2
= H20
[ΩM
(a0
a
)3+ ΩR
(a0
a
)4+ Ωk
(a0
a
)2+ ΩΛ
]
(a
a
)2
= H20
(a0
a
)2⇒ a(t) ∝ t
Ωr = 0
ΩM = 0
(= m)
t0 =1
H0= 13, 9× 109 H0 = 70
t0 =1
H0= 13, 9× 109 years,with H0 = 70 km/s/Mpc
a(t) = t
k = −1
a(t) ∝ t
η =nb
nγ
p↔ n
× ×
× ×•
!" !"d1 d2
d3
d4
#
$
#$
Ci−1,j−1 Ci,j−1
Ci,jCi−1,j
Ωb ≈ 0.3
(a
a
)2
= H20
(ΩM a−3 + ΩRa−4 + Ωka
−2 + ΩΛ)
(a
a
)2
= H20
[ΩM
(a0
a
)3+ ΩR
(a0
a
)4+ Ωk
(a0
a
)2+ ΩΛ
]
(a
a
)2
= H20
(a0
a
)2⇒ a(t) ∝ t
Ωr = 0
ΩM = 0
(= m)
t0 =1
H0= 13, 9× 109 H0 = 70
t0 =1
H0= 13, 9× 109 years,with H0 = 70 km/s/Mpc
a(t) = t
k = −1
a(t) ∝ t
η =nb
nγ
p↔ n
× ×
× ×•
!" !"d1 d2
d3
d4
#
$
#$
Ci−1,j−1 Ci,j−1
Ci,jCi−1,j
Milne Universe is the second “natural” universe
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Motivations
MotivationsSymmetry in Kerr-Newmann geometry under space, mass and charge reversal. Two spaces connected by the ringElementary particles as “black holes”B. Carter 66&68, Arcos & Pereira 04
In the following, antimatter gravitational mass is taken negative. Gravitational repulsion between matter and antimatter.
SNIa observations reveals effective repulsive gravity which is unexplained
High level of fine-tuning in standard model
Removes need for inflation
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Rencontres de Moriond 2008
Presentation of Milne Universe
The Symmetric Milne Universe
Age of the Milne Universe is almost exactly the same as the age of ΛCDM Universe
Ωb ≈ 0.3
(a
a
)2
= H20
(ΩM a−3 + ΩRa−4 + Ωka
−2 + ΩΛ)
(a
a
)2
= H20
[ΩM
(a0
a
)3+ ΩR
(a0
a
)4+ Ωk
(a0
a
)2+ ΩΛ
]
(a
a
)2
= H20
(a0
a
)2⇒ a(t) ∝ t
Ωr = 0
ΩM = 0
(= m)
t0 =1
H0= 13, 9× 109 H0 = 70
t0 =1
H0= 13, 9× 109 years,with H0 = 70 km/s/Mpc
a(t) ∝ t
η =nb
nγ
p↔ n
× × × ×•Ci−1 Ci Ci+1m
!"d1 !" d2
Ci Ci+1 Ci Ci+1
M(Ci−1) = 0, M(Ci) = m`1− d1
dx
´, M(Ci+1) = m
`1− d2
dx
´
dx
Age of the Universe was a problem for a Einstein-de Sitter model, which was solved by ΛCDM, but is also solved by Milne Universe
χ(z) =∫ a0
a01+z
da
aaz→+∞−→ +∞
χ(z) z→+∞−→ +∞
µ = m∗ −M + α(s− 1)− βc
η ≈ 8× 10−9
m∗, s, c :
M,α, β :
c
µ = −5 + 5 log(
dL(z)1
)
Pk =⟨|ρk|2
⟩k′ , k′ =
√k2
x + k2y + k2
z = k
ρ(x, y, z)
ρ(kx, ky, kz)
(a
a
)2
= H20 a−2.
χ2 =∑ (m∗ −M + α(s− 1)− βc− µth)2
σ2(µ) + σ2int
χ2/dof = 7.29
σ2int :
(k = −1)
a(t) =a(t)a0
mi = mgp = mga = −m miB = mp
B = maB = −m, (m ≥ 0)
As radial coordinate of a z redshift object: , a Universe with linear scale factor has no horizon. There is no need for an inflation scenario.
oldest globular clusters(Chaboyer et al.,98)
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Time scale of primordial Universe is extremely different !
Milne Universe spends much more time at high temperature than conventional Universe.
BBN duration:Standard BBN ≈ 200 secMilne BBN ≈ 30 years
Age of the Universe at recombinaison:14 Gy/1000 ≈ 14 My (compared to 0.38 My in ΛCDM)
BBN
CMB
4 x106
35
First noticed by Dev et al. 02
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Big-Bang Nucleosynthesis
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Rencontres de Moriond 2008
Big-Bang Nucleosynthesis
A. Coc et al., 2004
10-5
-3.5 -3 -2.5 -2 -1.5 -1 -0.5
WMAP( )
( )
[Si/H] or [O/H]
D/H
Upper(1!)
Mean(1!)
Q1009+2956 (Bur98)
PKS 1937-1009 (Tyt96)
HS 0105+1619 (OMe01)
Q2206-199 (Pet01)
Q0347-383 (DOd01)
Q1243+3047 (Kir03)
10-10
10-9
-3.5 -3 -2.5 -2 -1.5 -1 -0.5[Fe/H]
Li/H
Adopted (95% c.l.)(Ryan et al. 2000)
WMAPRyan et al. (1999)Ryan et al. (2000)
Thevenin et al. (2001)Bonifacio et al. (2002)
10-9
10-10
10-5
Predictions and observational status
16 Stellar Nucleosynthesis: 50 years after B2FH
0.22
0.23
0.24
0.25
0.26
WM
AP
!Bh
2M
ass
fracti
on
4He
10-2
10-6
10-5
10-4
3H
e/H
, D
/H
D
3He
10-10
10-9
1 10
7L
i/H
7Li
WM
AP
"!1010
Fig. 11. Abundances of 4He (mass fraction), D, 3He and 7Li (by number relative to H)
as a function of the baryon over photon ratio η (or Ωb·h2.) showing the effect of nuclearuncertainties.
during this period.Another question comes from recent observations of 6Li in the atmosphere of
A. Coc, 2007
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Rencontres de Moriond 2008
Big-Bang Nucleosynthesis in Milne Universe
Production of adequate He-4 is possible in coasting BBN. It needs a greater baryon to photon ratio
η ≈ 3 10−10
η ≈ 6 10−10
η ≈ 7× 10−9
n
p= e−Q/T ≈ 1
6
n
p≈ 1
6n
p≈ 1
7
m∗, s, c :
M,α, β :
c
Yp =2(n/p)
1 + (n/p)≈ 0.25
p + n↔ d + γ
µ = m−M = −5 + 5 log(
dL(z)1pc
)
µ = m−M = −5 + 5 log(
f(z, cosmologie)1
)
m−M = −5 + 5 log(
dL(z)1
)
Pk =⟨|ρk|2
⟩k′ , k′ =
√k2
x + k2y + k2
z = k
ρ(x, y, z)
ρ(kx, ky, kz)
(a
a
)2
= H20 a−2.
χ2 =∑ (m∗ −M + α(s− 1)− βc− µth)2
σ2(µ) + σ2int
Studied in Lohiya et al. (astro-ph/9902022) and Kaplinghat et al. (astro-ph/9805114)
Due to slower evolution, weak reactions decouple around 80 keV, maintaining equilibrium between protons and neutrons. Slowly, deuterium is formed and burnt into helium.Neutrons are regenerated to restore equilibrium value
Big-Bang Nucleosynthesis
BBN lasts in Milne Universe lasts 30 years instead of 3 minutes
No deuterium left
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In collaboration with A. Coc (CSNSM/Orsay)
Rencontres de Moriond 2008
Production of Deuterium and Lithium-6
Annihilation zone between domains of matter and antimatter is regulated by nucleon diffusion:
T ≥ 80 keV, massive annihilation by neutron diffusion
80 keV ≥ T ≥ 5 keV, no more neutrons, annihilation drops by a factor ≈ 104.
5 keV ≥ T ≥ 1 keV: Proton diffusion becomes efficient. Convection toward annihi lat ion zone . Nucleodisrupt ion and photodisintegration produce deuterium and lithium-6 by non-thermal reactions
1 keV > T: annihilation stops due to gravitational repulsion
Domain size: around 1015 m @ 1 keV (Mpc scale comoving)Deuterium production at the level of 10-5
BBN in presence of small-scale domains of antimatter studied in Jedamzik et al. 2001& Kurki Suonio et al. 2000
Big-Bang Nucleosynthesis
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Type Ia Supernovae
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Type Ia SN
SNLS Collaboration
(Astier et al. 06)
Rencontres de Moriond 2008
Einstein-de Sitter model seems totally ruled out
Milne Universe (blue) is very close to ΛCDM (green) as noted in Perlmutter et al. 99
Hubble diagram of Type Ia Supernovae
η ≈ 3 10−10
η ≈ 6 10−10
η ≈ 8× 10−9
n
p= e−Q/T ≈ 1
6n
p≈ 1
7
m∗, s, c :
M,α, β :
c
Yp =2(n/p)
1 + (n/p)≈ 0.25%
p + n↔ d + γ
µ = m−M = −5 + 5 log(
dL(z)1pc
)
µ = m−M = −5 + 5 log(
f(z, cosmologie)1
)
m−M = −5 + 5 log(
dL(z)1
)
Pk =⟨|ρk|2
⟩k′ , k′ =
√k2
x + k2y + k2
z = k
ρ(x, y, z)
ρ(kx, ky, kz)
(a
a
)2
= H20 a−2.
χ2 =∑ (m∗ −M + α(s− 1)− βc− µth)2
σ2(µ) + σ2int
χ2/dof = 7.29
Unknown parameter
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Absolute magnitude parameter M unconstrained for Milne
Type Ia SN
Which one is Milne ? Which one is ΛCDM ?
Rencontres de Moriond 2008
Residuals of Hubble diagram for the two models
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Res
idua
ls
Res
idua
lsredshift z redshift z
LCDM Best fit Milne - our analysis
Type Ia SN test most probably does not allow to exclude the Milne model !
Type Ia SN
Rencontres de Moriond 2008
Residues of Hubble diagram for the two modelsAbsolute magnitude parameter M unconstrained for Milne
14
Res
idua
ls
Res
idua
lsredshift z redshift z
Rencontres de Moriond 2008
CMB
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CMB
Position of the first acoustic peak in Milne Universe
In Milne Universe, spacetime is flat. Therefore space is hyperbolic, angular distance is drastically changed. An object in the sky will be seen with a much smaller angle than in standard cosmology
× ×
× ×•
!" !"d1 d2
d3
d4
#
$
#$
Ci−1,j−1 Ci,j−1
Ci,jCi−1,j
GM
c2R
ds2 = c2dt2 − a(t)2[
dr2
1− kr2+ r2
(dθ2 + sin2 θdφ2
)]
Gµν = Rµν −12Rgµν = 8πGTµν
cs =c√
3(1 + R), R =
3ρb
4ργ
∆θEdS
∆θMilne=
sinh(ln(1 + z))
2(1− 1√
1+z
) =z=1100
% 284
∆θ
∆θ=
2(1 = 1√
1+z
)
sinh(ln(1 + z))=
z=1100% 0.00352# 1.
θΛCDM
θMilne=
dMilneA (z)
dΛCDMA (z)
=z=1100
% 173
χ(z) =∫ a0
a01+z
da
aaz→+∞−→ +∞
dL = f(z, cosmologie)
χ(z) z→+∞−→ +∞
µ = m∗ −M + α(s− 1)− βc
rs =∫ trec
0csdη =
∫ trec
0cs
dt
a(t)
Angular scale of first peak corresponds to the angle under which is seen sound horizon at decoupling
rs =∫ ηrec
0csdη =
∫ trec
0cs
dt
a(t)
θ = rs/dA
θMilne ≈ 1.2
θMilne ≈ 1.2
rs =∫ trec
0cs
dt
a(t)
rs =∫ ηrec
η0
csdt
a(t)
rs =∫ trec
t170MeV
csdt
a(t)
θMilne
θΛCDM= 2.05
Ωb
Ωb ≈ 4 10−2
η ≈ 3 10−10
η ≈ 6 10−10
η ≈ 7× 10−9
n
p= e−Q/T ≈ 1
6
n
p≈ 1
6n
p≈ 1
7
m∗, s, c :
M,α, β :
c
Yp =2(n/p)
1 + (n/p)≈ 0.25
Sound generation during QGP transition, caused by matter-antimatter annihilation
rs =∫ ηrec
0csdη =
∫ trec
0cs
dt
a(t)
θ = rs/dA
θMilne ≈ 1.2
θMilne ≈ 1.2
rs =∫ trec
0cs
dt
a(t)
rs =∫ ηrec
η0
csdt
a(t)
rs =∫ trec
t170MeV
csdt
a(t)
θMilne
θΛCDM= 2.05
Ωb
Ωb ≈ 4 10−2
η ≈ 3 10−10
η ≈ 6 10−10
η ≈ 7× 10−9
n
p= e−Q/T ≈ 1
6
n
p≈ 1
6n
p≈ 1
7
m∗, s, c :
M,α, β :
c
Yp =2(n/p)
1 + (n/p)≈ 0.25
Finally, we obtain . One degree scale, just like the observed scale !
Angular distance
Sound horizon
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Preliminary conclusions
A symmetric matter-antimatter Milne universe requires neither inflation, nor Dark Energy, nor Dark Matter and is in surprisingly good agreement with main cosmological tests
BBN: good agreement for helium-4, realistic mechanism for deuterium and lithium-6 production at the observed levelsType Ia SN: Milne Universe very hard to distinguish from ΛCDM with current data
CMB: degree scale for first peak for Milne Universe !
Thank you
Still, a number of questions remain: - angular spectrum of temperature fluctuations (CMB),- is it possible to hide so many baryons ? (molecular gas ?)- consistency with other cosmological probes
Work under the direction of G. ChardinIn collaboration with A. Coc, E. Keihanen, J-J. Aly
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BACKUP SLIDES
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Two characteristic scales in Milne Universe- Sound horizon- Size of domains
BAO
Future experiments will be decisive to conclude on BAO.
Eisenstein et al. 05
19
Residues of Hubble diagram for the two models in SNLS analysis
LCDM Best fit Milne - SNLS analysis
Type Ia SN
Rencontres de Moriond 2008 20
Res
idua
ls
Res
idua
lsredshift z redshift z
LCDM Best fit Milne - our analysis
Type Ia SN test most probably does not allow to exclude the Milne model !
Type Ia SN
Rencontres de Moriond 2008
Residues of Hubble diagram for the two modelsAbsolute magnitude parameter M unconstrained for Milne
21
Res
idua
ls
Res
idua
lsredshift z redshift z
Rencontres de Moriond 2008
Type Ia SN
Milne ΛCDM
Without low redshift SN, Milne fit is slightly better !
22
Res
idua
ls
Res
idua
lsredshift z redshift z