exploring dark energy
DESCRIPTION
Lloyd Knox & Alan Peel University of California, Davis. Exploring Dark Energy. With Galaxy Cluster Peculiar Velocities. Exploring D.E. with cluster. Philosophy Advertisement Cluster velocity—velocity correlation functions as probes of dark energy POTENT on 100 Mpc scales. - PowerPoint PPT PresentationTRANSCRIPT
Exploring Dark Energy
With Galaxy Cluster Peculiar Velocities
Lloyd Knox & Alan Peel
University of California, Davis
Exploring D.E. with cluster
• Philosophy
• Advertisement
• Cluster velocity—velocity correlation functions as probes of dark energy
• POTENT on 100 Mpc scales
pecv
Observed apparent magnitude of SNe Ia
0m
Dark Energy Parameters
0 0 1, ( )x x x xw z w w z
Expansion rate, H(z)
Primordial P(k)
( )Ad z
Angular-diameter distance
( )Ld zLuminosity distance
( )D zGrowth factor
dV
dzdVolume element
0
2reion
, (1100),
, ,
mA
b
d
h z f
CMBlC
( )m zM
obs( )m z
Calibration parameters
noise
halo( , )N M z ( , )SZN y z
x-ray( , )N I z
lensinglC
Evolution of angular clustering
Alcock-Paczynski tests with
forest correlationsLy
Redshift-space correlations rot( , )N v zlens( , )N M z
Dark Energy
Models
Dark Energy Does Not Exist In A Vacuum
DASh (The Davis Anisotropy Shortcut)Dash is a combination of numerical computation with analytic and semi—analytic approximations which achieve fast and accurate computation.lC
How fast?About 30 times faster than CMBfast
How accurate?
rms error
Applications:
• parameter estimation (Knox, Christensen
& Skordis 2001, note: age and mcmc)
• error forecasting
Kaplinghat, Knox and Skordis (2002)
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On to peculiar velocities…
ikv 0( , ) ( ) ( , )x D x
v D
For 0.5, is much less dependent on the nature
of the dark energy than is the case for ( ) or r( ).
z D
D z z
Peculiar velocities may be helpful in breaking degeneracies.
,m w
continuity equation
Growth factor vs. z
(normalized to standard CDM)
Time derivative of growth factor vs. z
Dotted lines are for w=-0.7.
Solid lines are for w=-1
Measuring with the SZ effect pecv
Thermal
Kinetic
2 2
CMB
Spectral distortion characterized by Compton y parameter
( ) ( )
( ) ;
As 0, ( ) 2
T ee e
e e
k kTy dlT l n l
m c m c
I hyf x x
I kT
x f x
1
x
xSZ
I v e T vx
I c e T c
2
( / )Combine to get velocity: / e SZ
e
kT T Tv c
m c y
Sunyaev & Zeldovich 1980
Thermal SZKinetic SZ
Holzapfel et al. (1997)
A possible survey strategy
• Survey large area with large detector array at 30 GHz to find clusters.
• Follow up with a smaller array of detectors at 150 GHz and 220 GHz targeting the clusters. (Or maybe even FTS to get )
• Follow up with optical photometric or spectroscopic redshifts
eT
How well can be measured?pecv
Aghanim et al. (2001): Planck will result in cluster peculiar velocities with errors of 500 to 1,000 km/s.
These large errors are due to Planck’s big 5’ beam and noisy maps.
With a smaller beam a cluster stands out better against the confusing background of CMB anisotropy and other clusters.
1370880
815630
Abell 2163: 490 /
Abell 1689: 170 /
r
r
v km s
v km s
Holzapfel et al. (1997):
2 2CMB noise( ) ( )
25 km/sec (.01/ )2 Kv
T T
Haehnelt & Tegmark (1996)
Becker et al. (2001)
What Are The Expected Signals?
observer
Cluster 1
Cluster 2
1r
2r
r
1 2 1 2
1 22
1 2
( , , ) ( ) ( )
( )( ) ( )cos( ) ( ( ) ( ))
v r r
perp para perp
C z z v r v r
r r r rr r r
r r r
1 2 102
1 2 10 02
( )( ) ( )
2
( )( ) ( )[ ( ) 2 ]
2
perp
para
D D j krr dkP k
kr
D D j krr dkP k j kr
kr
10’ 15’ 30’ 60’
Expected correlation of radial component of velocities for clusters with the same redshift but in different directions
200 km/sec errors (16 micro-K for tau=0.01)
100 km/sec errors (8 micro-K for tau=0.01)
*Pierpaoli, Scott & White (2001)
*
1 2( , 1, 1)vC z z
Expected correlation of radial component of velocities for clusters in the same direction but with different redshifts1 2( 0, 1, )vC z z z
Note: redshifts may need to be determined to better than .01!
Velocity Bias
• Our calculations were for randomly selected locations in the Universe, but measurements will be made where clusters are bias
• Velocity bias not calculated yet (unpublished work by Sheth)
• Easily calculable.
POTENT on 100 Mpc scales
Bertschinger & Dekel 1989
We can reconstruct the gravitational potential from cluster peculiar velocities, as has been done with galaxy peculiar velocities, but with much cleaner velocity measurements.
*
*
Why?
• Use as input for better modeling of cluster and galaxy formation.
• Combine with other surveys to directly measure large—scale bias.
Gravitational Potential Reconstruction
2
,( , , ) ( ) ( ) ( , )lm l lml mr dkk k j kr Y
3 3 2 2' '
0 0
'( , ' ' ') ' ( ) ( ) '( ) '( ' )ll mm l l
k kW lmk l m k k k drr X r w r j kr j k r
H H
2/2( )
3m
m
a adDX r
da
Reconstruction weight:
Gravitational Potential Reconstruction
2 2
1 1( )v
v
dNw r
dr r
From G. Holder
350 km/s
k
4 ( )k P k
20,50,75,125,225l
Ignore these
Conclusions
• CMB is important for breaking degeneracies between dark energy parameters and other parameters
• DASh will be available soon.• Peculiar velocities are sensitive to• At • Cluster peculiar velocities can be measured very well (in
principle) for z > 0.2, well enough to measure the velocity correlations and reconstruct the large—scale gravitational potential.
• Theory/observable relationship is even more straightforward than other uses of clusters such as dN/dz.
( ) instead of ( )D z D z
0.5, ( ) is much more dependent on than .mz D z w
Thanks to G. Holder and S. Meyer for useful conversations