l. perivolaropoulos leandros.physics.uoi.gr department of physics university of ioannina
DESCRIPTION
Open page. Is ΛCDM the Correct Model?. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Structure of Talk. Model Classes - Key Questions. Geometric Constraints: Standard Rulers - Standard Candles. - PowerPoint PPT PresentationTRANSCRIPT
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L. Perivolaropouloshttp://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
Open page
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Model Classes - Key Questions
Geometric Constraints: Standard Rulers - Standard Candles
Comparison of Recent Standard Candle SnIa Data:-Figure of Merit-Consistency with ΛCDM-Consistency with Standard Rulers
Potential Conflicts of ΛCDM with Data:- Large Scale Velocity Flows- Cluster Halo Profiles- Emptiness of Voids - Brightness of High z SnIa
Conclusion
Dynamical Constraints: Linear Growth of Perturbations
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w z
z
1w
Dark Energy
Allowed Sector
w z
z
1w
Cosmological Constant
w z
z
1w
Modified Gravity
Allowed Sector
2
300
2 ln1 1( ) 3
( )1 1
X
Xm
d Hzp z dzw z
z Hz
H
Forbidden(ghosts)
1
'3 (1 ( '))
'~
ada
w aa
e
32
2 002
8( )
3 m
aa GH z a
a a
1
1a
z
Expansion History
Eq. of state evolution
G - g = T
G = TmT’μν)
G’ = Tm
2
300
2 ln1 1
3
1 1m
d Hz
dzw zH
zH
00
mm
cr
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Is General Relativity the correct theory on cosmological scales?
What is the most probable form of w(z) and what forms of w(z) can be excluded?
What is the consistency level of ΛCDM (GR + Λ) with cosmological observations?
What is the recent progress?
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Luminosity Distance (standard candles: SnIa,GRB):
24 L
Ll
d 0
( ) 1z
L th
dzd z c z
H z
: (0,1.7]
: [0.1,6]
SnIa z
GRB z
Angular Diameter Distance (standard rulers: CMB sound horizon, clusters):
sA
rd z
sr Ad z
0
( )1
z
A th
c dzd z
z H z
: 0.35, 0.2
: 1089
BAO z z
CMB Spectrum z
Ld z
SnIa Obs
GRB
flat
Direct Probes of H(z):
Significantly less accurate probesS. Basilakos, LP, MBRAS ,391, 411, 2008
arXiv:0805.0875
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2
10 , , 0 120 1 2
1
5log ( ) 5log ( ; , ), , min
L A i obs L A i th
mi
N
i
d z d z w ww w
Parametrize H(z): 0 1, 1,0CDM w w
Minimize:
Standard Candles (SnIa)
Standard Rulers (CMB+BAO)
Lazkoz, Nesseris, LP
JCAP 0807:012,2008. arxiv: 0712.1232
0 1 1
zw z w w
z
0 0.24m
ESSENCE (+SNLS+HST) data WMAP3+SDSS(2007) data
Chevallier, Pollarski, Linder
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Q2: What is the consistency of each dataset with ΛCDM?
Q3: What is the consistency of each dataset with Standard Rulers?
J. C. Bueno Sanchez, S. Nesseris, LP, 0908.2636
Q1: What is the Figure of Merit of each dataset?
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The Figure of Merit: Inverse area of the 2σ parameter contour. A measure of the effectiveness of the dataset in constraining the
given parameters.
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2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
2 .0 1 .5 1 .0 0 .5 0 .0
6
4
2
0
2
4
6
w 0
w1
SNLS ESSENCE GOLD06 UNION
CONSTITUTION WMAP5+SDSS5 WMAP5+SDSS7
0 0 28m .
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ESSENCE+SNLS+HST data
SNLS 1yr data
Trajectories of Best Fit Parameter Point
The trajectories of SNLS and Constitution clearly closer to ΛCDM for most values of Ω0m
Gold06 is the furthest from ΛCDM for most values of Ω0m
Q: What about the σ-distance (dσ) from ΛCDM?
Ω0m=0.24
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ESSENCE+SNLS+HST data
Trajectories of Best Fit Parameter Point
Consistency with ΛCDM Ranking:
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Consistency with Standard Rulers Ranking:
ESSENCE+SNLS+HST
Trajectories of Best Fit Parameter Point
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Consistency with ΛCDM Ranking
Consistency with Standard Rulers Ranking:
Identical Ranking Sequence!(Independent Criteria)
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Trajectories of Best Fit Parameter Point
0 1 1 4 2w ,w . ,
0 1 1 4 2w ,w . ,
Consistency with Dynamical Dark Energy Ranking:
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Consistency with ΛCDM Ranking: Consistency with Standard Rulers Ranking:
Consistency with Dynamical Dark Energy Ranking
Identical Ranking Sequence
Reversed Ranking Sequence
Tests Quality of SnIa Data
J. C. Bueno Sanchez, S. Nesseris, LP, 09082636
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Flat, ΛCDM remains at 1σ (or less) distance from the best fit with trend to further improve consistency with geometric probes
The 2σ parameter contour areas have improved by a factor of about 4 since 2005 while the number of filtered SnIa has increased by about the same factor. The consistency with standard rulers remains good
(except for Gold06 dataset)
Q: Which Dark Energy Probes have weak consistency with ΛCDM?
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Large Scale Velocity Flows
- Predicted: On scale larger than 50 h-1Mpc Dipole Flows of 110km/sec or less. - Observed: Dipole Flows of more than 400km/sec on scales 50 h-1Mpc or larger.- Probability of Consistency: 1%
Cluster and Galaxy Halo Profiles:
- Predicted: Shallow, low-concentration mass profiles- Observed: Highly concentrated, dense halos- Probability of Consistency: 3-5%
4 5virc ~
10 15virc ~
Bright High z SnIa:
- Predicted: Distance Modulus of High z SnIa close to best fit ΛCDM - Observed: Dist. Modulus of High z SnIa lower (brighter) than best fit ΛCDM - Probability of Consistency for Union and Gold06: 3-6%
The Emptiness of Voids:
- Predicted: Many small dark matter halos should reside in voids.- Observed: Smaller voids (10Mpc) look very empty (too few dwarf galaxies)- Probability of Consistency: 3-5%
From LP, 0811.4684
R. Watkins et. al. , 0809.4041
Broadhurst et. al. ,ApJ 685, L5, 2008, 0805.2617, S. Basilakos, J.C. Bueno Sanchez, LP., 0908.1333, PRD, 80, 043530, 2009.
LP and A. Shafielloo , PRD 79, 123502, 2009, 0811.2802
P.J.E. Peebles , astro-ph/0101127, Klypin et. al. APJ, 522, 82, 1999, astro-ph/9901240
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The dipole moment of large scale velocity flows (bulk flow) extends on scales up to 100h-1 Mpc with amplitude larger than 400km/sec.
ΛCDM predicted amplitude on scale larger than 50h-1 Mpc :
110km/sec
From R. Watkins, H. Feldman and M. J. Hudson, 0809.4041
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NFW profile:
4 2 0 2 4
0 .0
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
vir
s
rc
r
1c
2c
1 2c cΛCDM prediction:
The predicted concentration parameter cvir is significantly smaller than the observed.
From S. Basilakos, J.C. Bueno-Sanchez and LP,
PRD, 80, 043530, 2009, 0908.1333.
Data from:
Navarro, Frenk, White, Ap.J., 463,
563, 1996
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Parametrization:
6
11 : deCDM const
Measure growth function of cosmological perturbations:
mf a
Evolution of δ(sub-Hubble scales) :
James, Dutta, LP., 0903.5296
Horizon scales
Horizon scales
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Fit to LSS data:
ΛCDM provides an excellent fit to the linear perturbations
growth data
S. Nesseris, LP, Phys.Rev.D77:023504,2008
best fit
ΛCDM
0 0.3m
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The consistency of ΛCDM with geometric probes of accelerating expansion is very good and it appears to be further improving with
time.
There are a few puzzling potential conflicts of ΛCDM specific cosmological data mainly related with dynamical large scale structure
probes.
Data from dynamical probes on the linear growth of perturbations are currently not as constraining as geometric probes but they also have
good consistency with ΛCDM.