Transcript Accelerating Universe

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L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
1
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
Dynamical Constraints: Linear Growth of Perturbations
Conclusion
2
w z 
Cosmological Constant
Expansion History
z
w  1
3

a 2 8 G 
 a0 
H ( z)  2 
 0 m       a  
a
3 
a

2
Gmn - L gmn = k Tmn
a
w z 
1
1 z
Gmn = k Tmmn T’μν)
Dark Energy
z
Allowed Sector
p ( z)
w z  X

 X ( z)
a
 ~ e
3

1
da '
(1 w( a '))
a'
2
d ln H
1
1  z 
3
dz
2
3
 H0 
1 
 0 m 1  z 
 H 
w  1
Eq. of state evolution
Forbidden
(ghosts)
w z 
Modified
Gravity
0 m 
G’mn = k Tmmn
z
2
d ln H
1
1  z 
dz
w z  3
2
3
 H0 
1 
  0 m 1  z 
 H 
w  1
Allowed Sector
3
0 m
cr
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?
4
Direct Probes of H(z):
Luminosity Distance (standard candles: SnIa,GRB):
SnIa
GRB
Obs
dz 
d L ( z )th  c 1  z  
0 H  z 
SnIa : z  (0,1.7]
z
L
l
4 d L2
dL  z 
GRB : z  [0.1,6]
flat
Significantly less accurate probes
S. Basilakos, LP, MBRAS ,391, 411, 2008
arXiv:0805.0875
Angular Diameter Distance (standard rulers: CMB sound horizon, clusters):
dA  z 


rs
dA  z 
rs

c z dz 
d A ( z )th 

1

z
  0 H  z
BAO : z  0.35, z  0.2
CMB Spectrum : z  1089
5
LCDM   w0 , w1    1,0
Parametrize H(z):
w  z   w0  w1
z
1 z
Chevallier, Pollarski, Linder
Minimize:
5log10  d L, A ( zi )obs   5log  d L, A ( zi ; w0 , w1 )th 
  min
 2  m , w0 , w1    
2
2
N
i 1
ESSENCE (+SNLS+HST) data
i
WMAP3+SDSS(2007) data
Standard Candles
(SnIa)
Lazkoz, Nesseris, LP
0 m  0.24
JCAP 0807:012,2008.
arxiv: 0712.1232
Standard Rulers
(CMB+BAO)
6
Q1: What is the Figure of Merit of each dataset?
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
7
The Figure of Merit: Inverse area of the 2σ parameter contour.
A measure of the effectiveness of the dataset in constraining the
given parameters.
8
6
SNLS
4
w1
0
w1
2
0
6
GOLD06
ESSENCE
4
2
UNION
4
4
2
2
0
0
2
2
2
2
4
4
4
4
6
6
6
6
1.5
1.0
0.5
0.0
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0
w0
w0
6
2
2
0
4
6
w1
2
4
1.5
1.0
w0
0.5
0.0
1.0
0.5
0.0
0
2
4
6
6
2.0
1.5
WMAP5+SDSS7
4
2
2.0
6
4
2
0.0
w0
WMAP5+SDSS5
4
0
0.5
w0
6
CONSTITUTION
w1
2.0
w1
w1
6
w1
6
2.0
1.5
1.0
0.5
w0
0m  0.28
0.0
2.0
1.5
1.0
0.5
0.0
w0
9
Trajectories of Best Fit Parameter Point
ESSENCE+SNLS+HST data
Ω0m=0.24
SNLS 1yr data
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
10
Q: What about the σ-distance (dσ) from ΛCDM?
ESSENCE+SNLS+HST data
Trajectories of Best Fit Parameter Point
Consistency with ΛCDM Ranking:
11
ESSENCE+SNLS+HST
Trajectories of Best Fit Parameter Point
Consistency with Standard Rulers Ranking:
12
Consistency with ΛCDM Ranking
Consistency with Standard Rulers Ranking:
Identical Ranking Sequence!
(Independent Criteria)
13
Trajectories of Best Fit Parameter Point
 w0 ,w1    1.4,2

 w0 ,w1    1.4,2
Consistency with Dynamical Dark Energy Ranking:

14
Consistency with ΛCDM Ranking:
Consistency with Standard Rulers Ranking:
Identical Ranking Sequence
Tests Quality of SnIa Data
Reversed Ranking Sequence
Consistency with
Dynamical Dark Energy Ranking
J. C. Bueno Sanchez, S. Nesseris, LP, 09082636
15
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)
Flat, ΛCDM remains at 1σ (or less) distance from the best fit with
trend to further improve consistency with geometric probes
Q: Which Dark Energy Probes have weak consistency
with ΛCDM?
16
From LP, 0811.4684
R. Watkins et. al. , 0809.4041
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:
Broadhurst et. al. ,ApJ 685, L5, 2008, 0805.2617,
S. Basilakos, J.C. Bueno Sanchez, LP., 0908.1333, PRD, 80, 043530, 2009.
- Predicted: Shallow, low-concentration mass profiles
- Observed: Highly concentrated, dense halos  cvir ~ 10 15
- Probability of Consistency: 3-5%
Bright High z SnIa:
 cvir ~ 4  5
LP and A. Shafielloo , PRD 79, 123502, 2009, 0811.2802
- 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:
P.J.E. Peebles , astro-ph/0101127,
Klypin et. al. APJ, 522, 82, 1999, astro-ph/9901240
- Predicted: Many small dark matter halos should reside in voids.
- Observed: Smaller voids (10Mpc) look very empty (too few dwarf galaxies)
17
- Probability of Consistency: 3-5%
From R. Watkins, H. Feldman and M. J. Hudson, 0809.4041
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
18
Navarro, Frenk,
White, Ap.J., 463,
563, 1996
NFW profile:
From S. Basilakos, J.C. Bueno-Sanchez and LP,
PRD, 80, 043530, 2009, 0908.1333.
1.2
1.0
ΛCDM prediction:
c
c1  c2
rvir
rs
0.8
0.6
c1
0.4
0.2
c2
0.0
4
2
0
2
4
The predicted concentration parameter cvir is significantly
smaller than the observed.
Data from:
19
Measure growth function of cosmological perturbations:
Horizon scales
Evolution of δ
(sub-Hubble scales) :
f  m  a 
Parametrization:

Horizon scales
James, Dutta,
LP., 0903.5296
LCDM : de  L  const
 
6
11
20
Fit to LSS data:
0 m  0.3
ΛCDM
ΛCDM provides an excellent fit
to the linear perturbations
growth data
best fit
S. Nesseris, LP,
Phys.Rev.D77:023504,2008
21
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.
22