Overview of Large Scale Structure

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Overview of Large Scale Structure

• Uros Seljak
• Zurich/ICTP/Princeton/Berkeley/LBL
• Hamilton, may 16, 2007

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Outline

• Methods to investigate dark energy and dark
  matter galaxy clustering, cluster counts, weak
  lensing, Lya forest
• Issues of systematics and statistics
• Current constraints what have we learned so far,
  controversies
• What can we expect in the future?

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How to test dark energy?

• Classical tests redshift-distance relation (SN1A
  etc)
• Growth of structure CMB, Ly-alpha, weak lensing,
  clusters, galaxy clustering
• Scale dependence of structure (same tracers as
  above)

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Growth of structure by gravity

• Perturbations can be measured at different
  epochs
• CMB z1000
• 21cm z10-20 (?)
• Ly-alpha forest z2-4
• Weak lensing z0.3-2
• Galaxy clustering z0-2
• Sensitive to dark energy, neutrinos

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Scale dependence of cosmological probes
WMAP
CBI
ACBAR
Lyman alpha forest
SDSS
Galaxy clustering Weak lensing Cluster abundance
Complementary in scale and redshift
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Sound Waves from the Early Universe

• Before recombination
• Universe is ionized.
• Photons provide enormous pressure and restoring
  force.
• Perturbations oscillate as acoustic waves.

• After recombination
• Universe is neutral.
• Photons can travel freely past the baryons.
• Phase of oscillation at trec affects late-time
  amplitude.

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This is how the Wilkinson Microwave Anisotropy
Probe (WMAP) sees the CMB
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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 (in the
absence of curvature)
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Determining Basic Parameters
Matter Density Wmh2 0.16,..,0.33
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Determining Basic Parameters
Baryon Density Wbh2 0.015,0.017..0.031
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Current 3 year WMAP analysis/data situation
Current data favor the simplest scale invariant
model
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Galaxy and quasar survey
Galaxy surveys SDSS and 2dF
400,000 galaxies with redshifts
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Shape and acoustic Oscillations in the Matter
Power Spectrum

• Shape determined by matter and baryon density
• Amplitude not useful (bias)
• 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
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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
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Power Spectrum

• LRG analysis in Fourier space with a quadratic
  estimator for the power spectrum.
• See also FKP analysis in Percival et al. (2006).

Tegmark et al. (2006)
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Systematics nonlinear bias

• Need to model nonlinear bias
• Current analyses use Q model (Cole etal), where Q
  is either fixed from simulations (Q5-10 for
  normal galaxies, Q20-30 for LRGs in real space)
  or determined from the data by going to smaller
  scales (k0.3h/Mpc)
• Do NOT allow for Q to be free and only use
  klt0.1h/Mpc data (eg in Hamann etal 2007 they find
  even Q60-100 is acceptable, completely
  incompatible with the data at k0.2-0.3h/Mpc)
• Need to move to a better model, but it is
  uncertain how much we will gain for cosmology

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Are galaxy surveys consistent with each other?
Some claims that SDSS main sample gives more than
2 sigma larger value of W Need to account for
nonlinear bias
Fixing h0.7 Padmanabhan etal 2006
SDSS LRG photo 2dF SDSS main spectro
Bottom line no evidence for discrepancy if one
marginalizes over nonlinear bias, new analyses
improve upon SDSS main
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Sound Waves

• Each initial overdensity (in DM gas) is an
  overpressure that launches a spherical sound
  wave.
• This wave travels outwards at 57 of the speed
  of light.
• Pressure-providing photons decouple at
  recombination. CMB travels to us from these
  spheres.
• Sound speed plummets. Wave stalls at a radius of
  150 Mpc.
• Overdensity in shell (gas) and in the original
  center (DM) both seed the formation of galaxies.
  Preferred separation of 150 Mpc.

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A Standard Ruler

• The acoustic oscillation scale depends on the
  matter-to-radiation 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)!

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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 r23
• current 7000 deg2 of imaging data, 40 million
  galaxies
• 400,000 spectra (rlt17.77 main sample, 19.1
  QSO,LRG)

Image Credit Sloan Digital Sky Survey
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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 2dF comparable evidence
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Current BAO constraints

• SDSS LRG correlation function does show a
  plausible acoustic peak.
• Ratio of D(z0.35) to D(z1000) measured to 4.
• This measurement is insensitive to variations in
  spectral tilt and small-scale modeling. We are
  measuring the same physical feature at low and
  high redshift.
• Wmh2 from SDSS LRG and from CMB agree. Roughly
  10 precision.
• This will improve rapidly from better CMB data
  and from better modeling of LRG sample.
• Wm 0.273 0.025 0.123(1w0) 0.137WK.

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• Concept proposed for the Joint Dark Energy
  Mission (JDEM).
• 3/4-sky survey of 1ltzlt2 from a small space
  telescope, using slitless IR spectroscopy of the
  Ha line. SNe Ia to z1.4.
• 100 million redshifts 20 times more effective
  volume than previous ground-based surveys.
• Designed for maximum synergy with ground-based
  dark energy programs.
• Fisherology predicts 0.2 error on D_a over 1ltzlt2
• But do nonlinear effects spoil this? Smith etal
  2007 argue for 1-2 random noise on peak
  position! TBD
• SYSTEMATICS are key!

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Weak Gravitational Lensing
Distortion of background images by foreground
matter

Unlensed Lensed
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Weak Lensing Large-scale shear
Convergence Power Spectrum 1000 sq. deg.
to R 27 Huterer
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Gravitational Lensing
Refregier et al. 2002

• Advantage directly measures mass
• Disadvantages
• Technically more difficult
• Only measures projected mass-distribution
• Intrinsic alignments?

Tereno et al. 2004
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Weak lensing systematic errors

• PSF induced errors rounding (need to calibrate),
  ellipticity (use stars)
• Shear selection bias rounder objects can be
  preferentially selected
• Noise induced bias conversion from intensity to
  shear nonlinear
• STEP2 project bottom line current accuracy in
  best codes at 2-3 level, plenty of work to do to
  reach 1 level, not clear 0.1 even possible
• PHOTOz errors without spectroscopy easily a
  10-20 error (biasing sigma_8 high?), need
  complete spectroscopic surveys to the same depth!
  Currently this is only available for SDSS (DEEP2
  and zCOSMOS data)
• Intrinsic alignment has been detected and one
  MUST deal with it! Biasing sigma_8 low by 1-10
  (Hirata etal)

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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
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Intrinsic correlations in SDSS
300,000 spectroscopic galaxies, 36,000 LRGs No
evidence for II correlations Clear evidence for
GI correlations on all scales up to 60Mpc/h LRGs
show the strongest signal Gg lensing not
sensitive to GI
Mandelbaum, Hirata, Ishak, US 2005 Hirata etal
2006
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Implications for existing and future surveys
Up to 30 effect on power spectrum for shallow
survey at z0.5 2-20 effect for deep survey at
z1 current surveys underestimate s8 More
important for cross-redshift bins separate
redshift bins do not eliminate
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Galaxy clustering power spectrum shape
Galaxy clustering traces dark matter on large
scales Current results redshift space power
spectrum analysis based on 200,000 galaxies
(Tegmark etal, Pope etal, 2dF (Cole
etal) Padmanabhan etal LRG photometric power
spectrum analysis, 10 times larger volume, 2
million galaxies LRG spectro analysis Tegmark
etal, Eisenstein etal, Percival etal Amplitude
not useful (bias)
Nonlinear scales
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Galaxy bias determination

• Galaxies are biased tracers of dark matter the
  bias is believed to be scale independent on large
  scales (klt0.1-0.2/Mpc)
• If we can determine the bias we can use galaxy
  power spectrum to determine amplitude of dark
  matter spectrum s8
• High accuracy determination of s8 is important
  for dark energy constraints
• Weak lensing is the most direct method

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Galaxy-dark matter correlations galaxy-galaxy
lensing

• dark matter around galaxies induces tangential
  distortion of background galaxies extremely
  small, 0.1
• Specially useful if one has redshifts of
  foreground galaxies SDSS
• Express signal in terms of projected surface
  density and transverse separation r one
  projection less than shear-shear correlations
• with photozs not sensitive to intrinsic
  alignments
• - for LSS one needs to model cross-correlation
  coefficient between dark matter and galaxies
  simulations

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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/N30, the strongest weak lensing signal to date
testing ground for future surveys such as
LSST,SNAP
Seljak etal 2004
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Mandelbaum, US etal, in prep
2007previous attempts Hoekstra etal, Sheldon
etal
Preliminary, not yet properly calibrated Statistic
al error around 5 final systematic error is
likely to be smaller than for other weak lensing
analyses Alternative method to determine growth
rate with different systematics than shear-shear
correlations!
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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
• One of the few ways to probe dark energy
  clustering
• Future detections could be up to 6(10?) sigma,
  not clear if this probe can play any role in
  cosmological parameter determination

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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)

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• 2.5 sigma detection

Consistent with other probes
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Counting Clusters of Galaxies
Sunyaev Zeldovich effect X-ray emission from
cluster gas Optical data red sequence richness
Weak lensing (future?)
Simulations
growth factor
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Galaxy Cluster Abundance
Dependence on cosmological parameters
Sunyaev Zeldovich effect X-ray emission from
cluster gas Optical data red sequence richness
Weak lensing (future?)
of clusters per unit area and z
comoving volume
mass limit
mass function
mass function
Jenkins et al. 2001
Hubble volume N-body simulations in three
cosmologies cf Press-Schechter
growth function
power spectrum (?8, M-r)
overall normalization
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Pros and cons of cluster abundance

• Abundance very sensitive to cosmological
  parameters, specially sigma8
• Many different techniques to measure clusters
• Need to calibrate observable to halo mass
  simulations not yet reliable (resolution issues,
  turbulence, cosmic rays, magnetic fields)

• X-ray calibration not entirely reliable because
  clusters are not relaxed and may hve additional
  pressure support (cosmic rays, bulk motions)
• Weak lensing reliable on average, but scatter is
  an issue Malmquist and Eddington bias
• one can show that Malmquist bias dominates, only
  a robust lower limit on sigma8 can be established
  (Mandelbaum and US 2007)
• Studies that ignore scatter underestimate sigma8
• Self-calibration promising, but not for general
  M(L) relation

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Cluster abundance and masses with SDSS

• maxBCG and LRG cluster catalogs (20-30k cluster
  sample!)

It may be possible to give a lower limit from
cluster clustering
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Cosmic complementarity Supernovae, CMB, and
Clusters
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Ly-alpha forest as a tracer of dark matter and
dark energy
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 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
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Warm Dark Matter constraintsSeljak, Makarov,
McDonald, Trac, astro-ph/0602430

• Flux power spectrum
• 3000 SDSS spectra
• HIRES data probes smaller scales
• ?2(k) p-1 k P(k)
• 0.01 s/km 1 h/Mpc
• Colors correspond to redshift bins centered at z
  2.2, 2.4, , 4.2 (from bottom to top)

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SDSS Lya power spectrum analysis McDonald, US
etal 2006

• Combined statistical power is better than 1 in
  amplitude, comparable to WMAP
• 2ltzlt4 in 11 bins
• ?2 185.6 for 161 d.o.f.for SDSS
• A single CDM model fits the data over a wide
  range of redshift and scale
• WDM does not fit

Ly-alpha helps by reducing degeneracies between
dark energy and other parameters that Lya
determines well (amplitude, slope) Direct
search for dark energy at 2ltzlt4 reveals no
evidence for it
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WMAP vs. LyaF (vanilla 6 parameters)Linear amp.
slope constraints at z3, k0.009 s/km

• Green LyaF
• Red WMAP
• Black WMAP, SDSS-main, SN
• Yellow All
• Blue Viel et al. (2004) independent LyaF

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The amplitude controversy?

• Some probes, Ly-alpha, weak lensing, SZ clusters
  prefer higher amplitude (sigma_8gt0.85)
• Other probes, WMAP, X-ray cluster abundance,
  group abundance prefer lower amplitude
  (sigma_8lt0.80)
• Statistical significance of discrepancy is
  2.5?-sigma or less
• Most likely a combination of statistical
  fluctuations and residual systematic effects not
  modeled in one or more probes
• In Ly-alpha most studies find that astrophysics
  effects (winds, UV background fluctuations,
  reionization) on cosmological parameters are
  small, but more careful studies are needed

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Bispectrum measuring dark energy at zgt2
Partial degeneracy between UV background flux and
amplitude is broken, factor of 3 improvement in
amplitude Can determine power law slope of the
growth factor to 0.1 Mandelbaum etal
2003 Upcoming analysis on SDSS Slosar etal Will
provide a much better amplitude and hopefully
resolve the amplitude controversy Future of LYA
more data, nongaussian signal, 3-d analysis,
better modeling and simulations
Simulations, not yet real data
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Putting it all together

• Dark matter fluctuations on 0.1-10Mpc scale
  amplitude, slope, running of the slope
• Growth of fluctuations between 2ltzlt4 from Lya
• Lya very powerful when combined with CMB or
  galaxy clustering for inflation (slope, running
  of the slope), dark energy through growth rate
  comparison to zlt1 data, can also detect it
  directly if DE is significant for zgt2
• still important because it is breaking
  degeneracies with other parameters and because it
  is determining amplitude at z3.

US etal 04, 06
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Comprehensive cosmological parameter
analysisUS, Slosar, McDonald 2006

• CMB WMAP3, Boomerang-2k2, CBI, VSA, ACBAR
• Galaxies SDSS-main, SDSS-LRG (BAO), 2dF
• SN SNLS, Riess et al.
• LyaF SDSS, HIRES

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Dark energy constraints complementarity of
tracers
US, Slosar, McDonald 2006
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DE constraints degeneracies and dimension of
parameter space
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Time evolution of equation of state w
Individual parameters very degenerate
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Time evolution of equation of state

• w remarkably close to -1
• Best constraints at pivot z0.2-0.3, robust
  against adding more terms
• In a 3 parameter expansion error at pivot remains
  the same as for constant w

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To perturb or not to perturb dark energy

• Should one include perturbations in dark energy?
• For w-1 no perturbations, otherwise ignoring
  them not self-consistent (no gauge invariant way
  to ignore them), but close to w-1 a small effect
  if w is constant
• For wgt-1 perturbations in a single scalar field
  model with canonical kinetic energy, speed of
  sound c
• Non-canonical fields may give speed of sound ltltc
  
• For wlt-1 (phantom model) one can formally adopt
  the same, but the model has instabilities
• For w crossing from lt-1 to gt-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 wlt-1 (Creminelli etal 2006),
  perturbations in DE sector remain to be worked out

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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)

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A look at (almost dark) 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 m0.1-1eV free-streaming scale is gt10Mpc
• Neutrinos are quasi-relativistic at z1000 CMB
  is also important, opposite sign

m0.15x3, 0.3x3, 0.6x3, 0.9x1 eV
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New limits on neutrino mass

• WMAP3SDSS LyaSDSS2dFSN 6p
• Together with SK and solar limits
• Lifting the degeneracy of neutrino mass

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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, gtkeV. To suppress its abundance
  need small mixing angle, Qlt0.001, never
  thermalized

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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 mlt3.5-8keV (Abazajian
  2005, Boyarsky etal 2005)

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Sterile neutrino as dark matter

• To proceed we need to specify the model assume
  no generation of sterile neutrinos above GeV, no
  lepton asymmetry enhancements, only production
  through mixing
• First approximation production independent of
  momentum
• calculations in Abazajian (2005) give more
  accurate momentum distribution 10 weaker mass
  constraints relative to previous calculations
  which assume momentum distribution is the same as
  active
• The limits for this model can be easily modified
  to other models (mirror, thermal, entropy
  injection from massive steriles etc)

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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

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Future surveys and issues of statistics

• Weak lensing ground (Panstarrs, DES, LSST),
  space (SNAP, Dune)
• Cluster surveys SZ, X-rays, optical
• BAO APO-LSS, ADEPT
• Ly-alpha nothing dedicated but can be part of a
  general spectroscopic survey
• Beyond Fisherology in figure of merit there is
  realization noise in error predictions vs
  reality, more so for nongaussian distributions.
• Realization noise leads to weakening of predicted
  power in discriminating between models (because
  we can be unlucky in the realization)

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Realization noise
In some cases (eg, with positivity requirement) a
factor of two difference between Fisher
prediction and actual realization One should
report the realization noise in figure of merit
and two experiments within the error margin
should be deemed equal in power We need to focus
more on higher sigma contours, 3 and beyond!
Slosar and US, in prep
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Conclusions

• LSS can probe dark energy through a number of
  techniques, including galaxy clustering, weak
  lensing and their cross-correlations, cluster
  abundance and clustering and Ly-alpha forest
• 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.
• Future prospects many planned space and ground
  based missions, this may lead to a factor of
  several improvements in dark energy parameters
  like w, w.
• Systematics, systematics, systematics, statistics
• Much to be learned, but there remains much work
  to do for everyone involved