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L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
The consistency level of LCDM with geometrical data probes has been
increasing with time during the last decade.
There are some puzzling conflicts between ΛCDM predictions and dynamical data
probes
(bulk flows, alignment and magnitude of low CMB multipoles,
alignment of quasar optical polarization vectors, cluster halo profiles)
Most of these puzzles are related to the existence of preferred anisotropy axes
which appear to be surprisingly close to each other!
The axis of maximum anisotropy of the Union2 SnIa dataset is also located close to the
other anisotropy directions. The probability for such a coincidence is less than 1%.
The amplified dark energy clustering properties that emerge in
Scalar-Tensor cosmology
may help resolve the puzzles related to
amplified bulk flows and cluster halo profiles.
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
3
CDM   w0 , w1    1,0
Parametrize H(z):
w  z   w0  w1
z
1 z
Chevallier, Pollarski, Linder
5log10  d L, A ( zi )obs   5log  d L , A ( zi ; w0 , w1 )th  
  min
2
  m , w0 , w1    
2
i
i 1
2
N
Minimize:
ESSENCE (+SNLS+HST) data
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)
4
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,
JCAP 0911:029,2009, 0908.2636
5
w( z )  w0  w1
0 m  0.28
z
1 z
The Figure of Merit: Inverse area of the 2σ CPL parameter contour.
A measure of the effectiveness of the dataset in constraining the given
parameters.
6
SNLS
4
w1
0
4
2
2
0
0
2
2
2
2
4
4
4
4
6
6
6
6
2.0
1.5
1.0
0.5
0.0
w0
6
1.5
1.0
0.5
0.0
2.0
1.5
CONSTITUTION
1.0
0.5
2.0
0.0
6
4
4
4
2
2
2
0
4
4
6
6
2.0
1.5
w0
1.0
w0
0.5
0.0
0
2
4
6
2.0
w0
0.0
WMAP5+SDSS7
WMAP5+SDSS5
2
0.5
w0
6
2
1.0
w0
w0
UNION2
0
1.5
w0
w0
w1
w1
2.0
w0
w0
w1
UNION
4
w1
w1
0
w1
2
6
GOLD06
ESSENCE
4
2
w1
6
w1
6
1.5
1.0
w0
w0
0.5
0.0
2.0
1.5
1.0
w0
w0
0.5
0.0
The Figure of Merit: Inverse area of the 2σ CPL parameter contour.
A measure of the effectiveness of the dataset in constraining the given
parameters.
C
SDSS
MLCS2k2
G06
SNLS
SDSS5
SDSS7
Percival et. al.
Percival et. al.
E
U1
SDSS
SALTII
U2
Trajectories of Best Fit Parameter Point
ESSENCE+SNLS+HST data
Ω0m=0.24
SNLS 1yr data
The trajectories of SNLS, Union2 and Constitution are clearly
closer to ΛCDM for most values of Ω0m
Gold06 is the furthest from ΛCDM for most values of Ω0m
8
Q: What about the σ-distance (dσ) from ΛCDM?
ESSENCE+SNLS+HST data
Trajectories of Best Fit Parameter Point
Consistency with ΛCDM Ranking:
9
ESSENCE+SNLS+HST
Trajectories of Best Fit Parameter Point
Consistency with Standard Rulers Ranking:
10
From LP, 0811.4684,
I. Antoniou, LP 1007.4347
Large Scale Velocity Flows
R. Watkins et. al. , 0809.4041
- 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%
Alignment of Low CMB Spectrum Multipoles
M. Tegmark et. al., PRD 68, 123523
(2003), astro-ph/0302496
- Predicted: Orientations of coordinate systems that maximize all  al l of CMB
maps should be independent of the multipole l .
- Observed: Orientations of l=2 and l=3 systems are unlikely close to each other.
- Probability of Consistency: 1%
2
Large Scale Alignment of QSO Optical Polarization Data
2
D. Hutsemekers et. al.. AAS, 441,915
(2005), astro-ph/0507274
- Predicted: Optical Polarization of QSOs should be randomly oriented
- Observed: Optical polarization vectors are aligned over 1Gpc scale along a preferred axis.
- 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  c
- Observed: Highly concentrated, dense halos  cvir ~ 10 15
- Probability of Consistency: 3-5%
vir
~ 4  5
Three of the four puzzles for
ΛCDM are related to the
existence of a preferred axis
QSO optical polarization angle along the diretction l=267o, b=69o
D. Hutsemekers et. al.. AAS, 441,915
(2005), astro-ph/0507274
Quasar
Align.
CMB
Octopole
Q1: Are there other cosmological data with
hints towards a preferred axis?
Q2: What is the probability that these
independent axes lie so close in the sky?
CMB
Dipole
CMB
Quadrup.
Quadrupole component of CMB map
M. Tegmark et. al., PRD 68, 123523
(2003), astro-ph/0302496
I. Antoniou, LP 1007.4347
Velocity
Flows
Octopole component of CMB map
Dipole component of CMB map
Z=1.4
Z=0
North Galactic Hemisphere
South Galactic Hemisphere
2. Evaluate Best Fit Ωm in each Hemisphere
Z=1.4
1. Select Random Axis
Union2 Data
Galactic Coordinates
(view of sphere from opposite directions
 m
3.Evaluate

Z=0
4. Repeat with several random axes
and find  max

Anisotropies for Random Axes
Union2 Data
North-South Galactic Coordinates
ΔΩ/Ω=
0.43
ΔΩ/Ω=
-0.43
Direction of Maximum Acceleration:
(l,b)=(306o,15o)
Anisotropies for Random Axes (Union2 Data)
View from above Maximum Asymmetry Axis
Galactic Coordinates
Minimum Acceleration:
(l,b)=(126o,-15o)
 max
 0.42 Maximum Acceleration Direction:

(l,b)=(306o,15o)
 max
 0.42

ΔΩ/Ω=
0.43
ΔΩ/Ω=
-0.43
Construct Simulated Isotropic Dataset:
1. Find best fit parameter 0m and zero
point ofcet  0
2. Keep same directions, redshifts and σμi as real Union2 data
3. Replace real distance modulus μobs(zi) by gaussian random distance moduli with
mean th  zi , 0 m , 0  and standard deviation σμi .
ΔΩ/Ω=0.43
ΔΩ/Ω=-0.43
Anisotropies for Random Axes (Isotropic Simulated Data)
View from above Maximum Asymmetry Axis (Galactic Coordinates)
1. Compare a simulated isotropic dataset with the real Union2 dataset by splitting
each dataset into hemisphere pairs using 10 random directions.
U2
2. Find the maximum levels of anisotropy
  0 m  max 


 0m 
I
  0 m  max 


 0m 
(Union2) and
(Isotropic) and compare them.
3. Repeat this comparison experiment 40 times with different simulated isotropic
data and axes each time.
Distribution of
 max

Maximum  m
Isotropic Data can Reproduce
the Asymmetry Level of
Union2 Data

after 10 trial axes
U2
I
 0 m  max 


 0 m 
  0 m  max 

  0.24  0.07

0m


 m
Max

 0.29  0.05
In about 1/3 of the numerical experiments (14 times out of 40)
I
U2
 0 m  max   0 m  max 

 

 0 m   0 m 
i.e. the anisotropy level was larger in the isotropic simulated data.
There is a direction of maximum anisotropy in the Union2 data (l,b)=(306o,15o).
U2
The level
  0 m  max 


 0m 
of this anisotropy is larger than the corresponding level of about 70% of
isotropic simulated datasets but it is consistent with statistical isotropy.
Real Data Test Axes
ΔΩ/Ω=0.43
Simulated Data Test Axes
ΔΩ/Ω=0.43
ΔΩ/Ω=-0.43
ΔΩ/Ω=-0.43
Q: What is the probability that these
independent axes lie so close in the sky?
Calculate:
Compare 6 real directions
with 6 random directions
Q: What is the probability that these
independent axes lie so close in the sky?
Simulated 6 Random Directions:
Calculate:
6 Real Directions (3σ away from mean value):
Compare 6 real directions
with 6 random directions
Distribution of Mean Inner Product of Six
Preferred Directions (CMB included)
The observed coincidence of the axes is a
statistically very unlikely event.
8/1000 larger
than real data
< |cosθij|>=0.72
(observations)
<cosθij>
Distribution of Mean Inner Product of Three
Preferred Directions (CMB excluded)
Even if we ignore CMB data the
coincidence remains relatively improbable
71/1000 larger
than real data
< |cosθij|>=0.76
(observations)
<cosθij>
• Anisotropic dark energy equation of state (eg vector fields)
(T. Koivisto and D. Mota (2006), R. Battye and A. Moss (2009))
• Horizon Scale Dark Matter or Dark Energy Perturbations (eg 1 Gpc void)
(J. Garcia-Bellido and T. Haugboelle (2008), P. Dunsby, N. Goheer, B.
Osano and J. P. Uzan (2010), T. Biswas, A. Notari and W. Valkenburg (2010))
• Fundamentaly Modified Cosmic Topology or Geometry (rotating universe, horizon scale
compact dimension, non-commutative geometry etc)
(J. P. Luminet (2008), P. Bielewicz and A. Riazuelo (2008), E. Akofor, A. P.
Balachandran, S. G. Jo, A. Joseph,B. A. Qureshi (2008), T. S. Koivisto, D. F. Mota,
M. Quartin and T. G. Zlosnik (2010))
• Statistically Anisotropic Primordial Perturbations (eg vector field inflation)
(A. R. Pullen and M. Kamionkowski (2007), L. Ackerman, S. M. Carroll and M. B. Wise (2007),
K. Dimopoulos, M. Karciauskas, D. H. Lyth and Y. Ro-driguez (2009))
• Horizon Scale Primordial Magnetic Field.
(T. Kahniashvili, G. Lavrelashvili and B. Ratra (2008), L. Campanelli (2009))
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:
27
Navarro, Frenk,
White, Ap.J., 463,
563, 1996
From S. Basilakos, J.C. Bueno-Sanchez and LP,
NFW profile:
PRD, 80, 043530, 2009, 0908.1333.
clustered dark energy
1.2
1.0
c
c1  c2
rvir
rs
0.8
0.6
c1
0.4
0.2
c2
0.0
4
2
0
2
4
Clustered Dark Energy can produce more concentrated halo
profiles
Data from:
28
Q: Is there a model with a similar expansion rate as ΛCDM but with
significant clustering of dark energy?
A: Yes. This naturally occurs in Scalar-Tensor cosmologies
due to the direct coupling of the scalar field perturbations
to matter induced curvature perturbations
J. C. Bueno-Sanchez, LP,
Phys.Rev.D81:103505,2010,
(arxiv: 1002.2042)
 m , pm 
Rescale Φ
General Relativity:
Z   1
Units:
8 G 1
Flat FRW metric:
Generalized Friedman equations:
tot  ptot
These terms allow for
superacceleration
(phantom divide crossing)
Curvature (matter) drives evolution of Φ
(dark energy) and of its perturbations.
Advantages:
• Natural generalizations of GR (superstring dilaton, Kaluza-Klein theories)
• General theories (f(R) and Brans-Dicke theories consist a special case of ST)
• Potential for Resolution of Coincidence Problem
• Natural Super-acceleration (weff <-1)
• Amplified Dark Energy Perturbations
Constraints:
Solar System
Cosmology
F, 2
F
F, 2
F
 104
t  t0
 O 1
F     1   f 2
 f  5,   1,  i  0.12
Oscillations (due to coupling to
ρm ) and non-trivial evolution
Effective Equation of State:
1 2
  U     F  2 HF
p 2
weff  z  

1 2

  U     3HF
2
Scalar-Tensor (λf=5)
weff
Minimal Coupling (λf=0)
z
Perturbed FRW metric (Newtonian gauge):
J. C. Bueno-Sanchez, LP,
Phys.Rev.D81:103505,2010,
(arxiv: 1002.2042)
F,   1
Anticorrelation
k
 H
a
No suppression on small scales!
Sub-Hubble GR scales
k
 H
a
F,  1
F,
k
 H
a
k
 H
a

F,  1
F,
k
 H
a
H 2 a2
A
0
2
k
Suppressed fluctuations on small scales!
(as in minimally coupled quintessence)
Scale Dependence of Dark Energy/Dark Matter Perturbations
 f  0,   1,  i  0.12
Minimal Coupling (F=1)
 f  5,   1,  i  0.12
Non-Minimal Coupling (F=1-λf Φ2)
Dramatic (105) Amplification on sub-Hubble scales!
Early hints for deviation from the cosmological principle and statistical
isotropy are being accumulated. This appears to be one of the most likely
directions which may lead to new fundamental physics in the coming years.
The amplified dark energy clustering properties that emerge in
Scalar-Tensor cosmology
may help resolve the puzzles related to
amplified bulk flows and cluster halo profiles.
Scale Dependence of Dark Matter Perturbations
 f  0,   1,  i  0.12
Minimal Coupling (F=1)
 f  5,   1,  i  0.12
Non-Minimal Coupling (F=1-λf Φ2)
10 % Amplification of matter perturbations on sub-Hubble scales!