Transcript Accelerating Universe

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L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
Introduction:
Review Geometric Dark Energy Probes and Recent Constraints
Potential Conflicts of ΛCDM with Data
Dynamical Probe δ(z):
GR + Newtonian Gauge
m  m  a 
Sub-Hubble approximation,
k>0.01h Mpc-1
GR,
m  m  a,k  Beyond Sub-Hubble: Linear
-1
k<0.01h Mpc
Growth Rate
d ln  m
f 
d ln a k  0.01 h Mpc1
Gauge Dependence of δm(a)
Conclusion
2
m  a  
3a 2 H  a 
   k ,a  
f a 
k2
1    k ,a  

3H 0 2  0 m 


ak 2 
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
3
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
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
w0
6
0.0
2.0
1.5
1.0
2
2
0
4
6
w1
2
4
1.5
1.0
w0
w0
0.5
0.0
1.0
0m  0.28
6
1.5
1.0
w0
0.5
0.0
w( z )  w0  w1
4
2.0
0.5
0
2
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
0.5
w0
w0
w1
2.0
w1
w1
0
w1
2
6
GOLD06
ESSENCE
4
2
w1
6
w1
6
0.0
2.0
1.5
1.0
w0
0.5
0.0
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.
SDSS5
SDSS7
Percival et. al.
Percival et. al.
5
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
6
Q: What about the σ-distance (dσ) from ΛCDM?
ESSENCE+SNLS+HST data
Trajectories of Best Fit Parameter Point
Consistency with ΛCDM Ranking:
7
ESSENCE+SNLS+HST
Trajectories of Best Fit Parameter Point
Consistency with Standard Rulers Ranking:
8
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)
9
- Probability of Consistency: 3-5%
Perturbed Metric:
Linear Einstein equations:
Generalized Poisson:
k
 H
a
Poisson
equation
a
 m  2  m  4 G   m
a
10
Sub-horizon scale approximation=Newtonian Result
Perturbed Metric:
Linear Einstein equations:
Generalized Poisson:
better
approximation
3a 2 H  a 
3H 020m
  a,k  

k2
ak 2
2
Dent, Dutta, Phys.Rev.D79:063516,2009
11
Comoving Hubble scale at early times when most growth occurs is much smaller
At recombination commoving
Hubble scale ~100 Mpc
Hubble scale
100Mpc
Recombination
Sub-Hubble approximation is hardly valid
at early times when most growth occurs!
Generalized Poisson:
Fourier Space
k
GR

 k Poisson
3a 2 H  a 
1
k2
2
Coordinate Space
 Newt  
GM
GM 
  GR  
e
r
ar
3Har
Yukawa potential with a Hubble scale cutoff
13
Conservation of matter stress energy tensor
Modified Poisson:
k2
  4 G   a    k ,a  f  k ,a 
a2
a
a
  2   4 Gf  k ,a    a    0
to be compared with
3a 2 H  a 
3H 020m
  a,k  

k2
ak 2
2
14
d ln 
Define the growth factor as f  d ln am
3a 2 H  a 
3H 020m
  a,k  

k2
ak 2
2
ak 2

H 02
 0
  0.55  ΛCDM
approximate standard solution
  finite
ak 2
 O 1
H 02
approximate
scale dependent solution
15
Dent, Dutta, LP, Phys.Rev.D80:023514,2009.
k  0.004 h Mpc1
k  0.01 h Mpc1
CDM
 m  0 .3
k  0.001 h Mpc1
Dent, Dutta, LP,
Phys.Rev.D80:023514,2009.
16
Use dynamical dark energy parametrization:
Trial growth parametrization:
Best fit to numerical GR solution:
Variation as scales changes
17
CDM
 m  0 .3
18
Dynamical Dark Energy
m  0.3
19
Line element in synchronous gauge:
Growth equation in synchronous gauge:
(matter local rest frame everywhere)
Exact result. No scale dependence!!
(can not pick up Hubble scale effects)
Growth equation in newtonian gauge:
(time slicing of isotropic expansion)
Scale dependence.
(can pick up Hubble scale effects)
Line element in conformal Newtonian gauge:
   
Q: What is the proper gauge to use when comparing with observations?
Hubble Scale H0 at z=0
Power Spectrum at z=0
Newtonian Gauge
Power Spectrum at z=0
Synchronous Gauge
Near the horizon power spectra in the two gauges
differ significantly.
Comoving line of sight distance
1/r(z)
Yoo, Fitzpatrick, Zaldarriaga,
Phys.Rev.D80:083514,2009. 0907.0707
Need an observable gauge invariant replacement of δm.
General Perturbed Metric:
Some benefits of Newtonian gauge:
The gauge invariant perturbation δGI :
 GI    3 1  w 
a
B  E
a
reduces to δmΝ in the Newtonian gauge (B=E=0).
The gauge invariant potential ϕ
obeys a scale dependent Poisson equation
reduces to Φ in the Newtonian gauge (B=E=0).
 4 G a2GI
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 with specific
cosmological data mainly related with dynamical large scale structure
probes.
On scales larger than about 100h-1 Mpc the sub-Hubble
approximation for the growth rate of perturbations δ(z) needs to
be improved by a scale dependent factor in the Newtonian gauge.
The growth rate of of perturbations δ(z) depends on the gauge
considered and this dependence becomes important on scales larger
than about 100h-1 Mpc .
23
The predicted observable (gauge invariant) matter perturbations
depend on the gauge dependent perturbations, on the perturbed metric
and on other observables
Yoo, Fitzpatrick, Zaldarriaga, 0907.0707
24
Need an observable gauge invariant replacement of δm.
Example:
The observed redshift of a source is not directly connected to the
scale factor at the time of emission due to the perturbed FRW metric
δz depends on peculiar velocity of
source and metric perturbations
Yoo, Fitzpatrick, Zaldarriaga, 0907.0707
Phys.Rev.D80:083514,2009
Observed redshift
Gauge invariant
Matter density at source
Mean matter density at
observed redshift z
Q: What is the
dynamical equation
for the evolution of
the gauge invariant
perturbation?
25
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
26