Feasibility of detecting dark energy using bispectrum

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Feasibility of detecting dark energy using
bispectrum

• Yipeng Jing
• Shanghai Astronomical Observatory

Hong Guo and YPJ, in preparation
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Exploring Dark Energy----Physical Principles

• Measuring the luminosity distance---standard
  candles
• Measuring the angular distance---standard rulers
• Measuring the shape of a known object
• Measuring the dynamical evolution of the
  structures----linear growth factor D(z)
• Dynamical DE or w(z) measuring the geometry or
  DM dynamics at z02

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(No Transcript)
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Basics about the bispectrum method to measure the
linear growth factor
Definition of the bispectrum
Density Fluctuation
Power spectrum
Bispectrum
Reduced Bispectrum
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General properties of bispectrum

• The quantity measures the correlation of the
  densities at three points in space
• It is vanished for Gaussian density fluctuation
  field
• But it is generated by gravitational clustering
  of matter
• It can be also induced by selecting the density
  field in a biased way (e.g. the galaxy density
  field)

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On sufficiently large scale
2nd order Perturbation Theory Q_m depends on the
shape of P(k) only
Bias Relation
Can measure D(z) through measuring b_1
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Why Bispectrum

• In principle, one can measure the growth factor
  by measuring the power spectrum and the
  bispectrum since D(z) 1/b, without relying on
  the assumptions on bias and dynamics etc measure
  sigma_8 and DE
• Bispectrum is of great use in its own right
  non-Gaussian features (inflation), bias factor
  (galaxy formation), nonlinear evolution

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The key problems when measuring the growth factor

• Nonlinear evolution of dark matter clustering
• Nonlinear coupling of galaxies to dark matter
• Is there any systematic bias in measuring D(z)?
  On which scales ?
• Feasibility to measure with next generation of
  galaxy surveys (especially for those at high
  redshift) ?
• Simulation requirementLarge volume and high
  resolution

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Cosmological N-body simulations at SHAO with
10243 particles (PP-PM, Jing et al. 2007)
Box size (Mpc/h) M_p (M_sun/h) realizations
LCDM1 150 2.2E7 3
LCDM2 300 1.8 E9 4
LCDM3 600 1.5 E10 4
LCDM4 1200 1.2 E 11 4
LCDM5 1800 4.0 E 11 4
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Distribution of dark matter and galaxies
---simulations
Galaxy distribution based on a semi-analytical
model (Kang et al. 2005). Red for E and blue for
S galaxies
Density of dark matter
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Test of the 2nd order Perturbation Theory
Valid on scales larger than that of k0.1 h/Mpc
(less than 10)
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Halo modelnot perfect but helpful
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Halo modelunderstanding the nonlinear evolution
(but two-halo term sensitive to upper limit in
the integral)
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Test of the bias model

• Using Semi-Analytic Model of Millennium
  Simulation (Croton et al. 2006) to build Mock
  sample of galaxies.
• mock galaxies 600 Mpc/h (3 realizations) and
  1200 Mpc/h (4 realizations)

500 Mpc/h
Millennium Simulation
1200 Mpc/h
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Probability of galaxies in halos
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Systematics a few percent level Non-linear Q_m
used Valid on slightly smaller scales (klt0.2
h/Mpc) Error bars need to be estimated carefully
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b2 may tell about galaxy formation Positive for
brightest galaxies (M_rlt-22.5), negative for
bright and faint galaxies
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Error bars of bispectrumare comparable to the
Gaussian fluctuation on large scales klt0.1 h/Mpc
(Dark Matter)
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Error bars of B_g comparable to the Gaussian
case Mock galaxies
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Preliminary conclusions

• 2nd perturbation theory for the bispectrum of
  dark matter is valid for klt0.1 Mpc/h at redshift
  0
• Also valid for variance Delta2(k)lt0.3 at high
  redshift
• The bias expansion valid on slightly larger
  scales (about lt0.1 Mpc/h)
• The error is close to the Gaussian one
• Unbiased measurement of b1 and b2, therefore,
  dark energy and galaxy formation, promising
• Feasibility study with ongoing redshift surveys,
  especially at high redshifts, is being
  undertaken
• Accurate prediction for Q_m needs to be done (cf.
  loop-corrections, Sccocimarro et al.)