The impact of non-linear evolution of the cosmological matter power spectrum on the measurement of neutrino masses

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The impact of non-linear evolution of the
cosmological matter power spectrum on the
measurement of neutrino masses

• TAUP 2007 _at_ Sendai
• Shun Saito
• Theoretical Astrophysics Group
• University of Tokyo, JAPAN
• collaboratorsMasahiro Takada (Tohoku Univ. )
• Atsushi Taruya (Tokyo Univ.)

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Outline

• Introduction
• - Necessity for calculation of non-linear
  regime
• Perturbative Approach
• - Basic idea of our method
• Non-linear Power Spectrum with neutrinos
• - Difference with the prediction of linear
  theory
• Fisher matrix analysis
• - How does our non-linear theory improve the
  constraint on neutrino masses for future galaxy
  redshift survey?
• Summary Future Work

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Massive Neutrinos Cosmology
Constraints of total neutrino masses are given by
cosmology.
background expansion history
affect the CMB angular power spectra or SN Ia data
(c.f.) WMAP3 only
Spergel et al (2006)
suppression of matter perturbation
affect matter power spectrum of large-scale
structure
Massive neutrinos contribute naturally to matter
perturbation, but do not contribute below the
free-streaming scale due to large velocity
dispersion.
Spergel et al (2006)
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Suppression of matter perturbation
dimensionless power
suppression !!
Baryon Acoustic Oscillations (BAOs)
calculated by Linear theory
Non-linear regime !!
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Non-linear theory improvement?
? The planned galaxy high-redshift surveys such
as WFMOS aim the Baryon Acoustic Oscillations
(BAOs). ? Neutrinos free-streaming scale is
comparable to BAO scale, which is around
non-linear regime. ? If we have Non-linear
Theory, the constraint on neutrino masses may be
improved over linear theory.
Our Work
? calculate the next-to-leading order correction
based on perturbation theory for mixed dark
matter model for the first time ? present the
parameter forecast using Fisher matrix analysis
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Formalism Perturbative Approach
baryon mixed dark matter (CDM Neutrino) fluid
approximation
The continuity Euler equation for and
are non-linear equations ? Perturbative
expansion of Continuity Euler equation
Assuming that neutrinos density contrast stay at
linear level, we calculate the next-to-leading
order, one-loop correction , only for CDM plus
baryon.
The effect of neutrinos appears only in
scale-dependent growth rate of linear
.
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one-loop corrections
From standard perturbation theory
Makino,Sasaki,Suto (1992)
The one-loop correction is roughly proportional
to the square of .
Note that the effect of neutrinos is entirely
encoded in .
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Non-linear power spectrum
dimensionless power
one-loop
The amplitude is enhanced by non-linear
gravitational evolution.
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Suppression factor
valid range
0.18 hMpc-1
_at_ z 3
0.69 hMpc-1
Jeong,Komatsu(2006)
error
linear
? More suppressed than linear theory ? Reduced
shot noise error
non-linear
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Fisher matrix analysis
lower limit for inverted mass hierarchy
lower limit for inverted mass hierarchy
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Summary Future Works
Summary

• We derive the non-linear power spectrum including
  the effect of neutrinos
• for the first time.
• We found that the signal and the suppression are
  enhanced by the non-linear gravitational
  evolution.
• The constraint on neutrino masses may be improved
  from our non-linear theory for future galaxy
  redshift surveys.

Future Work

• Discuss the validity of our theory, treatment of
  neutrinos, valid range of PT,
• linear bias, Gaussian statistics etc.
• For a more realistic forecast, MCMC method should
  be adopted.
• The improvement of constraint on neutrino masses
  by SDSS data.