Cosmic Deflections

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Cosmic Deflections

• Scott Dodelson
• Kev Abazajian, Rocky Kolb, Sabino Matarrese, Toni
  Riotto, Chaz Shapiro, Alberto Vallinotto, Martin
  White, Pengjie Zhang

University of Kentucky March 9, 2006
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Most of the Universe is Dark
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Dark Sector likely related to New Fundamental
Physics
Quantum fluctuations, extra dimensions, very
light scalar field,
Supersymmetry, Axions,
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Gravitational Lensing Sensitive to ALL Matter
Light does not follow a straight path through the
clumpy universe
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A Perfect Match
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1804 Astronomer Johann Soldner computes
deflection of light due to Sun
Straightforward exercise in Newtonian gravity to
show that particle passing within distance d of
point mass M gets deflected by angle 2GM/d
This is a Cheat Fma does not apply to massless
particles
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Over a hundred years later Einstein posits that
mass distorts space even light paths would be
affected
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Could this effect be detected?
Einstein writes to George Hale (Director of Mount
Wilson Observatory) in 1913. He mentions the
0.84 (2GM?/R?c2) deflection expected from the
Sun.
Wambsganss 1998
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The next total solar eclipse was August 21, 1914.
An expedition was sent to observe in the region
of greatest eclipse
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Russian Crimean Peninsula
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1914 was not a good time to start a scientific
expedition in Europe
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The astronomers were captured by Russian soldiers
and released a month later with no data
which in retrospect is a good thing. Einstein
improved his theory over the next several years.
He eventually concluded that the deflection
should be twice as large as the Newtonian result
And this was confirmed by the famous
expeditions in 1919.
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In cosmology, deflections are the results of
perturbations around a smooth universe
SDSS
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Lensing leads to magnification
Courtesy Patricia (Caltech)
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Can confound key measurements
Distance modulus is function of cosmology
Clocchiatti et al. 2005
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Order of Magnitude Estimate
Gravitational Potential
Shear
Comoving distance
First guess
Only Fourier modes contribute which do not vary
along line of sight
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Simulated experiment
Not important for current experiments but will
soon be an important source of noise
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Scatter increases with redshift. More objects
de-magnified, but more large magnifications.
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Cosmic scatter depends on cosmological parameters
Clustering Amplitude
Matter Density

• Can we extract cosmological parameters from the
  cosmic scatter?

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We have learned a lot from cosmic scatter in
other contexts
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This will be tougher need to assume something
about intrinsic scatter
We assume no knowledge of its amplitude, but that
it is constant in redshift
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Can get very tight constraints on ?8
More theory/simulations needed to include effects
of baryons
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Beware of nongaussianity of cosmic scatter
?m
?8
Leads to a bias of ??80.12
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First order cosmic deflection affects distance
modulus

• Important source of noise can it be cleaned?
• Might extract important information about
  clustering in the universe

Systematics
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Lensing produces elliptical images
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Faint Galaxies
Courtesy Josh Frieman
Background Source shape
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Weak Lensing of Faint Galaxies distortion of
shapes
Courtesy Josh Frieman
Foreground galaxy
Background Source shape
Note the effect has been greatly exaggerated here
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Lensing of real (elliptically shaped) galaxies
Courtesy Josh Frieman
Foreground galaxy
Background Source shape
Must add signal from a large number of
foreground galaxies
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Need to average small signal over many sources
3x3 field with over 300 sources, each sampled
with 1 resolution
Wittman et al. 2003
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Cosmic Shear field depends on cosmology one of
these has more matter than the other
Jain, Seljak, White (2000)
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We can compute the 2-point functions of this
distribution
Dodelson, Shapiro, White 2005
Curves
Points
N Body Simulations
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Four seminal measurements in 2000 dozen since
then
Van Waerbeke Mellier 2003
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Constraints on parameters
Amplitude of Matter fluctuations
Matter Density
Contaldi, Hoekstra, Lewis astro-ph/0302435
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Several Upcoming Surveys
Dark Energy Survey
Panstarrs
SNAP
LSST
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Shear is sensitive to dark energy in two ways

• Angular projection
• Evolution of Potential

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Interesting Degeneracies
Abazajian Dodelson 2003
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Notice the difference between these 2 pictures
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Until now, we have been doing first order
perturbation theory
Or have we?
Courtesy Martin White
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Review of First Order Calculation

• ? is shear ? comoving distance x? perpendicular
  deflection p is direction vector
• Solve 1st order geodesic eqn for f in terms of
  first order gravitational potential ?
• To be consistent, evaluate ? at undeflected x

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Tirade

• There are many nonlinear beyond first order
  contributions to shear
• Inconsistent to start from first order formula
  and extract these higher order terms

is clearly wrong! Yet, this is what everyone
does when they study lensing nongaussianity.
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Inconsistent to use nonlinear power spectrum

• Nonlinear power spectrum obtained by summing
  over all perturbative corrections to linear
  theory
• To be consistent, need to consider not only
  ?(2), but all other second order corrections
• A priori, this affects all current constraints,
  which come from small scale measurements

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Solve Second Order Geodesic Equation
Products of First Order Terms
Explicitly Second Order Term
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Explicitly Second Order Term is Long!
Appendix of Bartolo, Komatsu, Matarrese,
Riotto, Phys. Rep. (2004) contains explicit
expressions for second order Christoffel symbols,
?. Relevant components yield 50 terms second
order in (scalar, tensor, and vector) metric
perturbations!
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Result Second Order Corrections

• Nonlinear Evolution of ?
• Born Correction
• Lens-Lens Coupling
• Reduced Shear

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Or

• Were not as clever as we thought we were!

All these terms have been derived before
(although usually not included in analyses).
This work serves as a proof that these are the
only (second order) terms that need be considered.
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New effects change answer by up to 10 on very
small scales
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Need to include these effects for accurate
parameter determination

• Technical note This may be an underestimate for
  current experiments constrained llt3000

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How do we extract information from the
nonlinearities?

• Identify individual objects cluster finding
• Systematically compute higher order statistics

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Nonlinearities as Signal

• Several groups have shown that there is much
  cosmological information stored in the bispectrum
  (e.g., Hui 1999 Zaldarriaga Scoccimarro 2003,
  Takada Jain 2004)
• To linear order the bispectrum is zero
• So, these corrections are expected to be
  relevant for the bispectrum

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Claim Bispectrum as powerful as power spectrum

• Need to get accurate theoretical predictions
• How important are corrections (reduced shear,
  lens-lens coupling, Born correction)?

Takada Jain 2004
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Corrections beyond nonlinear ? make 10
difference

• Most important on large scales, where linear
  theory predicts zero

These corrections are crucial to include for
future surveys
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Conclusions

• Light does not travel in straight lines
• Cosmic deflections can lead to confusion noise,
  bias
• Cosmic deflections are also signal, from which
  we can extract info on cosmological parameters

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Cosmic scatter depends on the matter distribution
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