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Modern State of CosmologyModern State of Cosmology
VV..NN.. Lukash LukashAstro Space Centre of Astro Space Centre of
Lebedev Physics InstituteLebedev Physics Institute
Cherenkov Conference-2004
• Observational status• Structure formations• Initial conditions• Cosmological parameters• Degeneracies
h cb, nS
, 8
• Minimal model and its extensions• Problems
7.03.0
h3/1
m
bSn
7.0e8
Cosmic Hubble parameter
Tegmark et al., 2003
Observational status
0.02
Coincidence between two
scales:
LSS (DM) and CMB (DB)
LSS and CMB scales
z < zeq: 2~
1
1
za
3
1100
3200
z
z
rec
eq
2
eq
rec
eqeq
1k
recrecSrec
3
c
1k
Keq-1DM
Krec-1
B
x
,
LSS :
CMB :
13k
k
eq
rec
rec
eq
Message from the early Universe:
Baryon asymmetry is related to dark matter
Independent determination of initial and boundary conditions
Theory of gravitational instability
• Zero order(Hubble diagram)
• First order(density perturbations spectrum)
Cosmological model – in two functions
(t)a
)z,k(P
fc , fb , f FU (late) m X
Model IU (early) AS nS S AT nT
LSS spectrum
CMB spectrum k
dk)k(W)k(PС
)z,k(T)k(P)z,k(P 2IU FU
IU FU
+ ( T )
Data mapping in k-space
k
dk)k(Pd ii
data point :
k
dk)k(P)k(WС
window spectrum probability distribution in k space
CMB :
P(k)
104 k
Tegmark, Zaldarriaga, 2002
Tegmark, Zaldarriaga, 2002
Cosmological initial conditions
Generation of density perturbations in the very early Universe
• Seeds – quantum vacuum fluctuations of density (phonons)
• Parametric amplification of density perturbations in the expanding Universe – spontaneous creation of phonons,
k ~ kH ~ 1 mm-1
• Stretching inhomogeneities on cosmological scales by inflation,
k >> kH ~ 1100 Мpc-1
dxdxhdtdx,C2dtD21ds 222 aa
,BAh2
1 ,v;D1u i
aa HvAHvq
qdtH
aa
,G4 C2
a H
q
p 2
CC
p
2
3
H
H2
p2 2
2
Lagrangian theory of
q field (V.N.L., 1980):
In conformal coordinates:
,,
222 qqqL
a
0qq2H3q 2
2a
k
0qUq 2
qq a
aa
)(
)(UU
Observational constraints on inflationary models
V(): classification of potentials
)exp(~)(V
~)(V
:0V
Large field inflation
Small field inflation
(hybrid)-inflation
C
0 1V)(V
:0V
4c;4
1V)(V
:0)0(V,0V
2С
С0
Models and observational quantities (T/S - nS)
-inflation (=4)
Е.V.Mikheeva, V.N.Lukash, 2004
0,8 0,9 1,0 1,1 1,20,0
0,2
0,4
0,6
0,8
1,0
c=80
c=22
c=12
c=9
c=7
T/S
nS
M.Tegmark et al., 2003
V()~1-(/*)2
0.9
0.6
0.3
WMAP + SDSS r = -8nT T/S = 0.6 r
• Chaotic inflation:
m2 - solid grounds
4 - severe trouble
• If nS>1 - -inflation
nS<1 - «chaotic» or «new» or …
• Inflationary model will be recognized in
the nearest future
Minimal modelnS=1 0=1
T/S=0
f=0
degeneracies: geometry tensor neutrino
4 parameters of MM:(error bars <10%)
84.0
023.0
123.0
7.0
17.0
8
b
c
A large number of observational points (~ 2000) can be fitted by only four parameters of MM
Reionization puzzle
QSO end of reionization: z~10
Evolution of star formation: flat out to z~6
Most distant galaxy: z~10 QSO: z=6.41
Two reionization epochs ?z~20 (massive stars)
z~10 (normal stars, QSO)
Arguments for >0
• Hubble diagram: SN Ia (correction for metallicity?)
• Dynamics: ISW (galaxies at z~0.5)
• Structure: P(k)
z11
a
3.014.0
)2.0( 2
m
2
m
hm 2mm h
LSS CMB
Reiss et al., 2002
Riess et al., 2004
N.Kardashev, ApJ 150, L135 (1967)
Dynamical impact of vacuumcross-correlation between maps of galaxies and CMB
~~G4 m aa2 ,const
,-1а
m
m
4aa
4
3
2m2 Th
~H
Keq=aH~mh2=mh (h/Mpc)
,h~h
~H:eq22
m
2m22
a
a 2mh~
1
a
Structure argument(solid!)
CMB
LSS
... and counter-arguments
• Weak lensing (m~1)• Problems of CDM:
– absence of cusps in galaxy centres (stability of galaxy bars)
– absence of substructure in galaxy halos (stability of spiral pattern in galaxy disks)
– small number of low-massive galaxies– flat luminosity and correlation functions
of galaxies
Myers et al., 2003
Angular cross-correlation between distant QSOs
and nearby clusters of galaxies (APM/SDSS)
Substructure in galaxy halo(simulations)
Diemand et al., 2004
~r -
(1, 3/2)
Among best-fit models(WMAP & 2dF)
m=1, =0=0.2, c=0.7
H0= 45 km s-1 Mpc-1
↓contradiction:
• local H0 (6070 km s-1 Mpc-1)(SZ, gravitational lenses: 50 20)
• SN Ia• cluster evolution• Ly
Degeneracies in cosmological parameter space
(reason – bad data,
region – 10 % of ММ):
geometrical (mh2 ~ const, 0 )
tensor (nS ~ fb )
neutrino (m ~ f)
Geometrical degeneracy(0=1.010.02)
h05 = 0.7
T0 = 13.5 05/2 Gyrs
Hubble constant and the age of the Universe vs tot
Tegmark et al., 2003
Tegmark et al., 2003
If m<0.7 eV, then
• z<zrec (3T m: z 103 [m/0.7 eV])
h2 = m/93 eV < 0.02 bh2
• f / m < 0.2 (for mh2 > 0.1)
CMB ⇒ cbh2
m= cb+ , m(1- f)=const cb (fixed by CMB)
+ af = b
(m+ = 1, a = cb , b = 1 - cb)
+ 0.5 f = 0.65 0.1
Arhipova et al., 2002
73.0n m
66.0f7.0
Novosyadlyj et al., 2000
Cosmological parameters CMB LSS
no GW,
+GW, no +GW,,BBN
mh2 0.14 0.12 0.16
mh 0.2 0.17 0.25
bh2 0.021 0.025 0.020
fb 0.15 0.22 0.10
f - - 0.05
nS 1.0 1.1 1.1
T/S - 0.2 0.3
0 0 0
0.7 0.8 0.6
ConclusionsConclusions
• Breaking degeneracy between initial and boundary conditions in cosmology
• Stable prediction:
nS 1, 0, 0.60.7
• Best-fit model: f ~ fb ~ 10%, m ~ 0.4, h ~ 0.65
(MM: fb ~ 15%, m ~ 0.3, h~ 0.7)
• If m 0.3 , then 0, h 0.7
m > 0.3 , 0.1, h < 0.7
• ???
m 0.04 0.4 eV
(f<0.1: m <0.4 eV)
early ionization (z~20)
T/S 0.2
small C2, C3
distortions ~30, 200
high 2
the running parameter
Unsolved fundamental problems:
• Dark matter (multicomponent):
b , c~m~
• Cosmological constant: ~M4 = (10-3eV)4=
standard model: M ~1 TeV
GUT: M ~1013 GeV
quantum gravity: M ~1019 GeV
• Coincidence of СМВ and LSS scales
(relation between baryon asymmetry and dark matter)
• T/S → energy scale of inflation
2dF Galaxy Redshift Survey
O.Lahav et al., 2002
Beyond concordance model: opt ~ 0.17
• Low C2,3, deviations (>3) at l~30, 200
• Rolling of spectral index• Poor 2 of concordance model (others in 1)• Spectral excess at l~2500 (CBI, ACBAR)
QSO: end of reionization at z~6
Evolution of star formation: flat out to z~6
Most distant galaxy: z=6.56
QSO: z=6.41
New: two reionization epochs
At z~20 (massive stars, QSO)
At z~6 (normal stars, QSO)
T.Shanks, astro-ph/0401409
Cross-correlation between WMAP (94 GHz) and galaxy clusters (АСО, R2)
T.Shanks, astro-ph/0401409