Weak Lensing and Dark Energy Cosmology

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Weak Lensing and Dark Energy Cosmology

• Tong-Jie Zhang???
• Department of Astronomy, Beijing Normal
  University
• Cosmology Workshop
• Institute of High Energy Physics, Chinese Academy
  of Sciences
• 2008/12/08

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3-D Accelerating Universe
WMAP
3-D Universe 3 dark sides
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(1). Our UniverseDark energy
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(2). Dark Matter halo(????)
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(3). Dark ages(????)
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Outline

• 0. Basic of Gravitational lensing
• 1. Dark Energy and Neutrino Mass Constraints
  from WL, SN Ia and RGA
• 2. The signatures of BAOs on the convergence
• power spectrum of weak lensing.
• 3. Application of wavelet on Weak lensing

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0. Basic of Gravitational lensing
Schematic Diagram of Gravitational Lensing
(???????)
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Physics of Gravitational Lensing (GL)
Bending of Light under Gravity
Light will follow the straightest possible path
through flat space time. If spacetime is curved
near a massive object, so the trajectory of
light is also curved.
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Observational Event of of Gravitational Lensing
an Einstein ring galaxy directly behind a galaxy
Einsteins Cross
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HST Image of a gravitational lens in galaxy
cluster
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Category of GL

• Strong gravitational lensing
• Weak gravitational lensing

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Gravitational lens TheorySketch of a typical
gravitational lens system
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Deflection angle

• General Relativity for a point mass M

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Lensing equation or ray-trace equation
Position of source
Position of image
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Lensing equation
Position of source
Multiple images can be produced if lens is strong
Position of image
Tong-Jie Zhang ApJ 602, L5-8(2004)
astro-ph_at_0401040
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Convergence and shear
Kgt1 ? strongKltlt1 ? weak
Deflection potential
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Distortion and Magnification
Shear
Magnification
Critical curves in lens plane Caustics in
source plane
Det
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Strong lensing

• Sources are close to the caustic lines.
• K gt1 and rgt1 The convergence and shear are
  strong enough to produce giant arcs and multiple
  images.

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The probability for strong lensing
E(z) and f (M, z) dependent on cosmological
model
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CLASS observation

• The Cosmic Lens All-Sky Survey CLASS)
• An international (USA, UK and Netherlands)
  collaborative
• project to map more than 10,000 radio sources in
  order to create
• the largest and best studied statistical sample
  of gravitationally lensed systems.
• Sample
• Well-defined statistical sample 8958
• Multiply imaged sourses 13
• P_obN(gt\theta)/8958

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Lensing models

• SIS
• GNFW

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Image separation probability for GNFW model
Tong-Jie Zhang ApJ 602, L5-8(2004)
astro-ph_at_0401040
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Constraint on potential
Kyu-Hyun Chae et al ApJ 607, L71-74(2004)
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Weak lensing (cosmic shear)

• Cosmic shear is the distortion of the shapes
  of background galaxies due to the bending of
  light by the potentials associated with
  large-scale structure in the universe.

Wek lensing regime K ltlt1 and rltlt1
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Distortion of background images shape and
correlation
Before lensed
After lensed
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Measurement

• The ellipticity of galaxy and the intrinsic
  ellipticity and shear

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Weak lensing shear spin-2 polarization field
F
The mean expectation of source ellipticities and
alignment
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Shear component

• The tangential shear and the 45 degree
  rotated shear in the local frame defined by
  the line connecting the pair of galaxies

b
b
a
a
a
?
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Shear correlation function
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Two-point cosmic shear statistics
1. shear correlation
2. the top-hat filtered variance of the shear
3. the variance of the aperture-mass
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Power spectrum of convergence
OCDM
?CDM
?CDM (linear)
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Observational Constraint on cosmology

• H. Hoekstra, Y. Mellier, L. van Waerbeke, E.
  Semboloni, L. Fu et al, The Astrophysical
  Journal, 647116127, 2006

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Joint constraint using WL and CMB
Contaldi et al, PRL, 90, 2003
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1. Dark Energy and Neutrino Mass Constraints
from WL, SN Ia and RGA

• Yan, Gong, Tong-Jie Zhang, Tian Lan and Xue-Lei
  Chen
• (astro-ph_at_arXiv 0810.3572) Sumitted to ApJ

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The existence of non-zero neutrino masses

• has been established firmly by the experiments
  detecting
• 1. atmospheric neutrinos,
• 2. solar neutrinos
• 3. reactor neutrinos
• 4. accelerator beam neutrinos

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• The neutrinos were still relativistic at the
  decoupling epoch.
• However, they are definitely non-relativistic at
  the present epoch, as the neutrino oscillation
  experiments have shown.
• Therefore, the matter density must contain the
  neutrino contribution when they are
  non-relativistic,

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Current constraints on neutrino mass
F.D.Bernardis et al. 2008
WMAP5
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WMAP5 Results on neutrino

• WMAP5

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Weak Leasing and Neutrino Mass
Free streaming effect
,
W. Hu D. J. Eisenstein, 1998, ApJ
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• The massive neutrinos could suppress the matter
  power spectrum on small scales, due to their free
  streaming, thus reducing the convergence power
  spectrum of the weak lensing, which is sensitive
  to the small scale matter distribution.
• Weak lensing is therefore a powerful measurement
  for both the dark energy and the massive
  neutrinos.

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The Likelyhood of WL
Shear correlation function (Crittenden et al.
2002)
The likelyhood
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Other Likelyhood
,

• SN Ia
• RGA
• BAO

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Data sets

• Weak lensing data
• CFHLST-wide, 22 deg2 (Fu et al. 2008)
• RCS, 53 deg2 (Hoekstra et al. 2002)
• SN Ia data
• SCP Union data, 307 samples (Kowalski et
  al. 2008)
• RGA (relative galaxy ages)
• H(z) from GDDS, 9 samples (Simon et al.
  2005)
• BAO data
• A at z0.35 (Eisenstein et al. 2005)

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1. Weak Lensing Constraints on w
Results

• Weak constraint on
• w for current WL data
• WLSNRGABAO
• w -1.0 0.19 -0.21
• at 95.5 C.L.
• (w -1.0 0.14 -0.11 for WMAP5)
• The similar degeneracy
• direction and constraint
• ability for SN Ia and RGA

wCDM
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2. Weak Lensing Constraints on Smv
Smvlt0.4eV
Smvlt0.8eV
at 95.5 C.L.
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3. Constraints on w and Smv

• Weak degeneracy
• between w andSmv

• Compatible and
• comparable with the
• results of WMAP5

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2. The signatures of BAOs on the convergence
power spectrum of weak lensing

• In the early universe prior to recombination, the
  free electrons couple the baryons to the photons
  through Compton interactions, so these three
  species move together as a single fluid.
• The primordial cosmological perturbations on
  small scales excite sound waves in this
  relativistic plasma, which results in the
  pressure-induced oscillations and acoustic peak.

• The memory of these baryon acoustic oscillations
  (BAOs) still remain after the epoch of
  recombination.

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Two Effect of BAO after the epoch of recombination

• 1. The BAOs leave their imprints through the
  propagating of photons on the last scattering
  surface and produce a harmonic series of maxima
  and minima in the anisotropy power spectrum of
  the cosmic microwave background (CMB) at z1000.
• 2. Due to the significant fraction of baryons
  in the universe, BAOs can also be imprinted onto
  the latetime power spectrum of the
  non-relativistic matter.

Acoustic Oscillations in theEarly Universe and
Today Christopher J. Miller,1 Robert C. Nichol,1
David J. Batuski222 JUNE 2001 VOL 292 SCIENCE
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BAO on the latetime power spectrum of the
non-relativistic matter

• BAOs can give rise to the wiggles in the matter
  power spectrum
• (a). Correlation function of galaxies (z0)
• (b). The power spectrum of 21 cm emission
  generated from the neutral hydrogen from the
  epoch of reionization through the underlying
  density perturbation
• (c). The power spectrum gravitaional lensing
  strong and weak

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(a). BAO on Correlation function of
galaxies(z0) Sound Waves in Matter

• 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
  about 100 Mpc.
• Overdensity in shell (gas) and in the original
  center (DM) both seed the formation of galaxies.
  Preferred separation of 100 Mpc.

100 Mpc
D. J. Eisenstein et al., Astrophys. J. 633, 560
(2005)
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(b). BAO on the power spectrum of 21 cm emission
Xiao-Chun Mao and Xiang-Ping Wu, ApJ, 673
L107L110, 2008
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(c). BAO on the power spectrum gravitational
lensing weak
The matter power spectrum
Tong-Jie Zhang, Qiang Yuan, Tian Lan
astro-ph_at_arXiv0812.0521
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The convergence power spectrum of weak lensing
Tong-Jie Zhang, Qiang Yuan, Tian Lan
arXiv0812.0521
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The statistical errors in themeasurements of
weak lensing power spectrum
Tong-Jie Zhang, Qiang Yuan, Tian Lan
astro-ph_at_arXiv0812.0521
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Conlusions

• 1. The BAOs wiggles can be found in both of
  the linear and nonlinear convergence power
  spectra of weak lensing at about 40 lt llt 600,
  but they are weaker than that of matter power
  spectrum.
• 2. Although the statistical error for LSST are
  greatly smaller than that of CFHT and SNAP survey
  especially at about 30 lt l lt 300, they are still
  larger than the their maximum variations of BAOs
  wiggles.
• 3. Thus, the detection of BAOs with the ongoing
  and upcoming surveys such as LSST, CFHT and SNAP
  survey confront a technical challenge.

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3. Application of wavelet on Weak lensing

• Construction of Convergence
• Theoretical expression

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N-body simulation parameters

• Itanium Beowulf cluster at CITA
• 10243 mesh resolution
• 5123 particles
• output periodic surface density maps at 20482
  resolution
• an initial redshift z_i50, 1000 steps
• comoving box size L200h-1 Mpc

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Parameters

• a Hubble constant h0.7
• A scale invariant n1 initial power spectrum
• A flat cosmological model with \Omega_m
  \Lambda 1
• \Omega_m0.3
• \sigma_80.82

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Stacking of map (here just a example)
Produce
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(No Transcript)
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Wavelet

• Pls see papers written by Prof.Fang Li-Zhi
• such as
• 1. Fang Li-zhi and W. Thews Wavelet in
  Physics. Would Scientific Singapore
• 2. Fang Li-zhi et als papers appeared in ApJ.

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Non-Gaussianity

• In the standard model of cosmology, fluctuations
  start
• off small, symmetric, and Gaussian. Even in
  some non-Gaussian models such as topological
  defects, initial fluctuations are still
  symmetric positive and negative fluctuations
  occur with equal probability.
• As fluctuations grow by gravitational
  instability, this
• symmetry can no longer be maintained
  overdensities can be arbitrarily large, while
  underdense regions can never have less than zero
  mass. This leads to Non-Gaussianity in the
  distribution of matter fluctuations.

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Non-Gaussianity using wavelet
Skewness and Kurtosis
No significant non-Gaussianity can be identified
from the third and fourth order cumulants.
Jesús Pando, David Valls-Gabaud, and Li-Zhi
Fang, PRL, Vol. 81, p. 4568-4571 ( 1998)
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Weak lensing
R360/2j arcmins J_max11 for 2048
Tong-Jie Zhang, Ue-Li Pen, Li-Zhi Fang, in
preparation for submitting to ApJ
The significant non-Gaussianity can be identified
on small scale.
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My appeared papers related to Lensingstrong or
weak

• (1). Reconstruction of the One-Point Distribution
  of Convergence from Weak Lensing by Large-Scale
  Structure
• Zhang Tong-Jie Pen Ue-Li
• The Astrophysical Journal ApJ, Volume 635,
  Issue 2, pp. 821-826 (12/2005)
• (2) Gravitational Lensing by Dark Matter Halos
  with Nonuniversal Density Profiles
• Zhang, Tong-Jie
• The Astrophysical Journal ApJ, Volume
  602, Issue 1, pp. L5-L8.(02/2004)
• (3). Optimal Weak-Lensing Skewness Measurements
• Zhang, Tong-Jie Pen, Ue-Li
  Zhang, Pengjie Dubinski, John
• The Astrophysical Journal ApJ, Volume 598,
  Issue 2, pp. 818-826. (12/2003)
• (4). Detection of Dark Matter Skewness in the
  VIRMOS-DESCART Survey Implications for Omega0
• Pen, Ue-Li Zhang, Tongjie
  van Waerbeke, Ludovic Mellier, Yannick
  Zhang, Pengjie Dubinski, John
• The Astrophysical Journal ApJ, Volume 592,
  Issue 2, pp. 664-673. (08/2003)
• Thanks!