State of the (dark)
universe report
Uros Seljak
Zurich/ICTP/Princeton
Heidelberg, november 7, 2006
Outline
1) Methods to investigate dark energy and dark
matter: SN, CMB, galaxy clustering, cluster
counts, weak lensing, Lya forest
2) Current constraints: what have we learned so
far, controversies
3) What can we expect in the future?
Context
1. Conclusive evidence for acceleration of the Universe.
Standard cosmological framework  dark energy (70% of mass-energy).
2. Possibility: Dark Energy constant in space & time (Einstein’s L).
3. Possibility: Dark Energy varies with time (or redshift z or a = (1+z)-1).
4. Impact of dark energy can be expressed in terms of “equation of state”
w(a) = p(a) / r(a) with w(a) = -1 for L.
5. Possibility: GR or standard cosmological model incorrect.
6. Whatever the possibility, exploration of the acceleration of the Universe
will profoundly change our understanding of the composition and nature
of the Universe.
How to test dark
energy/matter?
1) Classical tests: redshift- luminosity
distance relation (SN1A etc), redshiftangular diameter distance, redshiftHubble parameter relation
Classical cosmological tests (in a new form)
Friedmann’s (Einstein’s)
equation
How to test dark
energy/matter?
1) Classical tests: redshift-distance
relation (SN1A etc)…
2) Growth of structure: CMB, Ly-alpha,
weak lensing, clusters, galaxy clustering
Growth of structure by gravity
Perturbations can
be measured at
different epochs:
1.CMB z=1000
2. 21cm z=10-20 (?)
3.Ly-alpha forest
z=2-4
4.Weak lensing
z=0.3-2
5.Galaxy clustering
z=0-1 (3?)
Sensitive to dark
energy, neutrinos…
How to test dark
energy/matter?
1) Classical tests: redshift-distance
relation (SN1A etc)…
2) Growth of structure: CMB, Ly-alpha,
weak lensing, clusters, galaxy clustering
3) Scale dependence of structure
Scale dependence of cosmological probes
z  1088
WMAP
CBI
ACBAR
Lyman alpha forest
z 0
SDSS
Complementary in scales and redshift
z 3
Sound Waves from the
Early Universe
Before recombination:
Amplitude
– Universe is ionized.
– Photons provide enormous
pressure and restoring force.
– Perturbations oscillate as
acoustic waves.
Same Initial
Phase
After recombination:
– Universe is neutral.
– Photons can travel freely past
the baryons.
– Phase of oscillation at trec
affects late-time amplitude.
Maximal Effect
Time
Minimal Effect
Recombination
This is how the Wilkinson Microwave
Anisotropy Probe (WMAP) sees the
CMB
Determining Basic
Parameters
Angular Diameter
Distance
w = -1.8,..,-0.2
When combined with
measurement of matter
density constrains data to a
line in Wm-w space
Determining Basic
Parameters
Matter Density
Wmh2 = 0.16,..,0.33
Determining Basic
Parameters
Baryon Density
Wbh2 = 0.015,0.017..0.031
also measured through D/H
Current 3 year WMAP analysis/data situation
Current data favor the simplest scale
invariant model
400,000 galaxies with redshifts
Galaxy and quasar survey
Sloan Digital Sky Survey (SDSS
• 2.5 m aperture
• 5 colors ugriz
• 6 CCDs per color,
2048x2048, 0.396”/pixel
• Integration time ~ 50 sec
per color
• Typical seeing ~ 1.5”
• Limiting mag r~23
• current 7000 deg2 of
imaging data, 40 million
galaxies
• 400,000 spectra
(r<17.77 main sample,
19.1 QSO,LRG)
Image Credit: Sloan Digital Sky Survey
Galaxy power spectrum: shape analysis
Galaxy clustering traces dark
matter on large scales
Current results: redshift space
power spectrum analysis based
on 200,000 galaxies (Tegmark
etal, Pope etal), comparable to
2dF (Cole etal)
Padmanabhan etal: LRG power
spectrum analysis, 10 times
larger volume, 2 million
galaxies
Amplitude not useful (bias
unknown)
Nonlinear
scales
Are galaxy surveys
consistent with each other?
Some claims that SDSS main sample gives more
than 2 sigma larger value of W
Fixing h=0.7
SDSS LRG photo
2dF
SDSS main spectro
Bottom line: no evidence for discrepancy,
new analyses improve upon SDSS main
Acoustic Oscillations in the
Matter Power Spectrum
• Peaks are weak;
suppressed by a factor
of the baryon fraction.
• Higher harmonics
suffer from diffusion
damping.
• Requires large surveys
to detect!
Linear regime matter power spectrum
A Standard Ruler
• The acoustic oscillation scale
depends on the matter-toradiation ratio (Wmh2) and the
baryon-to-photon ratio
(Wbh2).
• The CMB anisotropies
measure these and fix the
oscillation scale.
• In a redshift survey, we can
measure this along and across
the line of sight.
• Yields H(z) and DA(z)!
dr = DAdq
dr = (c/H)dz
Observer
Baryonic wiggles
Best evidence: SDSS
LRG spectroscopic
sample (Eisenstein etal
2005), about 3.5 sigma
evidence
SDSS LRG photometric
sample (Padmanabhan,
Schlegel, US etal 2005):
2.5 sigma evidence
To perturb or not to perturb dark
energy
• Should one include perturbations in dark energy?
• For w=-1 no perturbations
• For w>-1 perturbations in a single scalar field model with canonical
kinetic energy, speed of sound c
• Non-canonical fields may give speed of sound <<c
• For w<-1 (phantom model) one can formally adopt the same, but the
model has instabilities
• For w crossing from <-1 to >-1 it has been argued that the
perturbations diverge: however, no self-consistent model based on
Lagrangian exists
• There is a self-consistent ghost condensate model that gives w<-1
(Creminelli etal 2006) and predicts no perturbations in DE sector
Weak Gravitational Lensing
Distortion of background images by foreground matter
Unlensed
Lensed
Weak Lensing: Large-scale shear
Convergence
Power
Spectrum
1000 sq. deg.
to R ~ 27
Huterer
Gravitational Lensing
Refregier et al. 2002
– Advantage: directly measures mass
– Disadvantages
• Technically more difficult
• Only measures projected massdistribution
• Intrinsic alignments?
Tereno et al. 2004
Shear-intrinsic (GI) correlation
Hirata and US 2004
•
•
•
•
•
Same field shearing is also tidally distorting, opposite sign
What was
is now , possibly an order of magnitude increase
Cross-correlations between redshift bins does not eliminate it
B-mode test useless (parity conservation)
Vanishes in quadratic models
Lensing shear
Tidal stretch
Intrinsic correlations
in SDSS
Mandelbaum, Hirata, Ishak, US etal 2005
300,000 spectroscopic
galaxies
No evidence for II
correlations
Clear evidence for GI
correlations on all scales up
to 60Mpc/h
Gg lensing not sensitive to GI
Implications for future surveys
Mandelbaum etal 2005, Hirata and US 2004
Up to 30% for
shallow survey at
z=0.5
10% for deep
survey at z=1:
current surveys
underestimate s8
More important for
cross-redshift bins
Galaxy bias determination
b (k ) =
2
Pgg (k )
Pdm (k )
•Galaxies are biased tracers of dark matter;
the bias is believed to be scale independent
on large scales (k<0.1-0.2/Mpc)
•If we can determine the bias we can use
galaxy power spectrum to determine
amplitude of dark matter spectrum s
•High accuracy determination of s is
important for dark energy constraints
•Weak lensing is the most direct method
8
8
galaxy-galaxy lensing
• dark matter around galaxies
induces tangential distortion
of background galaxies:
extremely small, 0.1%
Useful to have redshifts of
foreground galaxies: SDSS
Express signal in terms of
projected surface density and
transverse r
Signal as a function of
galaxy luminosity, type…
Galaxy-galaxy lensing measures galaxy-dark
matter correlations
Goal: lensing determines halo
masses (in fact, full mass
distribution, since galaxy of a
given L can be in halos of
different mass)
Halo mass increases with galaxy
luminosity
SDSS gg: 300,000 foreground
galaxies, 20 million background,
S/N=30, the strongest weak
lensing signal to date
testing ground for future surveys
such as LSST,SNAP
Seljak etal 2004
dark matter corr function
On large scales
galaxies trace dark
matter
G-g lensing in
combination with
autocorrelation analysis
gives projected dark
matter corr. function
Mandelbaum, US etal, in prep
WMAP-LSS cross-correlation: ISW
Detection of a signal indicates time changing gravitational
potential: evidence of dark energy if the universe IS flat.
•Many existing analyses (Boughn and Crittenden, Nolta etal,
Afshordi etal, Scranton etal, Padmanabhan etal)
•Results controversial, often non-reproducible and evidence
is weak
•Future detections could be up to 6(10?) sigma, not clear if
this probe can play any role in cosmological parameter
determination
WMAP-SDSS cross-correlation: ISW
N. Padmanabhan, C. Hirata, US etal 2005
•4000 degree overlap
•Unlike previous
analyses we combine
with auto-correlation
bias determination
(well known redshifts)
•2.5 sigma detection
QuickTime™ and a
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QuickTime™ and a
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Consistent with other probes
Ly-alpha forest as a
tracer of dark matter
Basic model: neutral hydrogen (HI) is determined by ionization
balance between recombination of e and p and HI ionization from
UV photons (in denser regions collisional ionization also plays a
role), this gives
2
r HI  r gas
Recombination coefficient depends on gas temperature
Neutral hydrogen traces overall gas distribution, which traces dark
matter on large scales, with additional pressure effects on small
scales (parametrized with filtering scale kF)
Fully specified within the model, no bias issues
SDSS Lya power spectrum analysis
McDonald, US etal 2005
• Combined statistical
power is better than 1%
in amplitude, comparable
to WMAP
• 2<z<4 in 11 bins
• 2 ≈ 129 for 104 d.o.f.
• A single model fits the
data over a wide range
of redshift and scale
Ly-alpha helps by reducing degeneracies between dark energy and other
parameters that Lya determines well (amplitude, slope…)
Direct search for dark energy at 2<z<4 reveals no evidence for it
The amplitude controversy
• Some probes, Ly-alpha, weak lensing, SZ clusters
prefer high amplitude (sigma_8>0.85)
• Other probes, WMAP, X-ray cluster abundance,
group abundance… prefer low amplitude
(sigma_8<0.75)
• Statistical significance of discrepancy is 2.5?sigma or less
• For the moment assume this is a statistical
fluctuation among different probes and not a sign
of a systematic error in one or more probes
Putting it all together
US etal 04, 06
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Dark matter fluctuations on
0.1-10Mpc scale: amplitude,
slope, running of the slope
Growth of fluctuations
between 2<z<4 from Lya
Lya very powerful when
combined with CMB or galaxy
clustering for inflation (slope,
running of the slope), not
directly measuring dark energy
unless DE is significant for z>2
 still important because it is
breaking degeneracies with
other parameters and because it
is determining amplitude at
z=3.
Dark energy constraints:
complementarity of tracers
US, Slosar, McDonald 2006
DE constraints: degeneracies and
dimension of parameter space
Time evolution of equation of state w
Individual parameters very degenerate
Time evolution of equation of state
•
w remarkably close to 1
• Best constraints at
pivot z=0.2-0.3, robust
against adding more
terms
• error at pivot the same
as for constant w
• Perturbations switched
off
What if GR is wrong?
• Friedman equation (measured through distance)
and growth rate equation are probing different
parts of the theory
• For any distance measurement, there exists a w(z)
that will fit it. However, the theory can not fit
growth rate of structure
• Upcoming measurements can distinguish Dvali et
al. DGP from GR (Ishak, Spergel, Upadye 2005)
• (But DGP is already ruled out)
•
A
look
at
neutrinos
Neutrino mass is of great importance in
particle physics (are masses
degenerate? Is mass hierarchy
inverted?): large next generation
experiments proposed (KATRIN…)
•
Neutrino free streaming inhibits
growth of structure on scales smaller
than free streaming distance
•
If neutrinos have mass they are
dynamically important and suppress
dark matter as well, 50% suppression
for 1eV mass
For m=0.1-1eV free-streaming scale is
>10Mpc
Neutrinos are quasi-relativistic at
z=1000: CMB is also important, opposite
sign
•
•
m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV
New limits on neutrino mass
• WMAP3+SDSS Lya+SDSS+2dF+SN 6p:
• Together with SK and solar limits:
• Lifting the degeneracy of neutrino mass
Neutrino as dark matter
• Initial conditions set by inflation (or something similar)
• Neutrino free streaming erases structure on scales smaller than free
streaming distance
• For neutrino to be dark matter it must have short free streaming
length: low temperature or high mass
• We can put lower limit on mass given T model
• One possibility to postulate a sterile neutrino that is created through
mixing from active neutrinos. This is natural in a 3 right handed
neutrinos setting, two are used to generate mass for LH, 3rd can be
dark matter. To act like CDM need high mass, >keV. To suppress its
abundance need small mixing angle, Q<0.001, never thermalized
Sterile neutrino as dark
matter
• A sterile neutrino in keV range could be the dark matter and could
also explain baryogenesis, pulsar kicks, seems very natural as we
need sterile neutrinos anyways (Dodelson and Widrow, Asaka,
Shaposhnikov, Kusenko, Dolgov and Hansen…)
• However, a massive neutrino decays and in keV range its radiative
decays can be searched for in X-rays. If the same mixing process is
responsible for sterile neutrino generation and decay then the
physics is understood (almost, most of the production happens at
100MeV scale and is close or above QCD phase transition)
• Strongest limits come from X-ray background and COMA/Virgo
cluster X-rays and our own galaxy, absence of signal gives m<3.58keV (Abazajian 2005, Boyarsky etal 2005)
Results and implications
•
•
•
Combined with the 6keV (COMA), 8-9keV (Virgo, X-ray background)
upper limit from radiative decays THIS model is excluded
How do the constraints change with possible entropy injection that
dilutes sterile neutrinos relative to CMB photons/active neutrinos?
T is decreased relative to CMB, neutrinos are colder
•
Dilution requires larger mixing angle for same matter density, so decay
rate higher, which makes X-ray constraints tighter
•
•
This does not open up the window
To solve the model need to generate neutrinos with additional
interactions at high energies above GeV
•
Future as seen by the dark side
Membersof the universe task force
Andy Albrecht, Davis
Gary Bernstein, Penn
Bob Cahn, LBNL
Wendy Freedman, OCIW
Jackie Hewitt, MIT
Wayne Hu, Chicago
John Huth, Harvard
Mark Kamionkowski, Caltech
Rocky Kolb, Fermilab/Chicago
Lloyd Knox, Davis
John Mather, GSFC
Suzanne Staggs, Princeton
Nick Suntzeff, NOAO
Techniques
Four techniques at different levels of maturity:
a.
BAO only recently established. Less affected by astrophysical
uncertainties than other techniques.
b.
CL least developed. Eventual accuracy very difficult to predict.
Application to the study of dark energy would have to be built upon a
strong case that systematics due to non-linear astrophysical
processes are under control.
c.
SN presently most powerful and best proven technique. If photo-z’s
are used, the power of the supernova technique depends critically on
accuracy achieved for photo-z’s. If spectroscopically measured
redshifts are used, the power as reflected in the figure-of-merit is
much better known, with the outcome depending on the ultimate
systematic uncertainties.
d.
WL also emerging technique. Eventual accuracy will be limited by
systematic errors that are difficult to predict. If the systematic errors
are at or below the level proposed by the proponents, it is likely to be
the most powerful individual technique and also the most powerful
component in a multi-technique program.
Systematics
Our inability to forecast reliably systematic error levels is the biggest
impediment to judging the future capabilities of the techniques. We need
a.
b.
c.
d.
BAO– Theoretical investigations of how far into the non-linear regime the data
can be modeled with sufficient reliability and further understanding of galaxy
bias on the galaxy power spectrum.
CL– Combined lensing and Sunyaev-Zeldovich and/or X-ray observations of
large numbers of galaxy clusters to constrain the relationship between galaxy
cluster mass and observables.
SN– Detailed spectroscopic and photometric observations of about 500
nearby supernovae to study the variety of peak explosion magnitudes and
any associated observational signatures of effects of evolution, metallicity, or
reddening, as well as improvements in the system of photometric calibrations.
WL– Spectroscopic observations and narrow-band imaging of tens to
hundreds of thousands of galaxies out to high redshifts and faint magnitudes
in order to calibrate the photometric redshift technique and understand its
limitations. It is also necessary to establish how well corrections can be made
for the intrinsic shapes and alignments of galaxies, removal of the effects of
optics (and from the ground) the atmosphere and to characterize the
anisotropies in the point-spread function.
Future Probes
Four types of next-generation projects have been considered:
a.
an optical Large Survey Telescope (LST), using one or more of the
four techniques
b.
an optical/NIR JDEM satellite, using one or more of four techniques
c.
an x-ray JDEM satellite, which would study dark energy by the cluster
technique
d.
a Square Kilometer Array, which could probe dark energy by weak
lensing and/or the BAO technique through a hemisphere-scale survey
of 21-cm emission
Each of these projects is in the $0.3-1B range, but dark energy is not the
only (in some cases not even the primary) science that would be done by
these projects.
13. Each of these projects considered (LST, JDEM, and SKA) offers
compelling potential for advancing our knowledge of dark energy as part
of a multi-technique program. The technical capabilities needed to
execute LST and JDEM are largely in hand.
Findings
The Stage IV experiments have different risk profiles:
a.
SKA would likely have very low systematic errors, but needs technical
advances to reduce its cost. The performance of SKA would depend
on the number of galaxies it could detect, which is uncertain.
b.
Optical/NIR JDEM can mitigate systematics because it will likely
obtain a wider spectrum of diagnostic data for SN, CL, and WL than
possible from ground, incurring the usual risks of a space mission.
c.
LST would have higher systematic-error risk, but can in many
respects match the statistical power of JDEM if systematic errors,
especially those due to photo-z measurements, are small. An LST
Stage IV program can be effective only if photo-z uncertainties on very
large samples of galaxies can be made smaller than what has been
achieved to date.
A mix of techniques is essential for a fully effective Stage IV program. No
unique mix of techniques is optimal (aside from doing them all), but the
absence of weak lensing would be the most damaging provided this
technique proves as effective as projections suggest. Combining all
information can lead to a factor of 3 improvement on w, w’ each.
Conclusions
• Dark energy remarkably similar to cosmological constant,
w=-1.04+/- 0.06, no evidence for w evolution or modified gravity
• Best constraints achieved by combining multiple techniques: this is
also needed to test robustness of the results against systematics.
• Dark matter best described as cold and collisionless: no evidence
for warm dark matter (sterile neutrinos)
• Neutrinos not yet detected cosmologically, but getting really close
to limits from mixing experiments: unlikely to be degenerate and
inverted hieararchy is mildly disfavored (at one sigma…)
• Future prospects: many planned space and ground based missions,
this will lead to a factor of several improvements in dark energy
parameters like w, w’.