Nonlinear matter power spectrum to 1% accuracy between dynamical dark energy models

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Non-linear matter power spectrum to 1 accuracy
between dynamical dark energy models

• Matt Francis
• University of Sydney
• Geraint Lewis (University of Sydney)
• Eric Linder (Lawrence Berkeley National
  Laboratory)
• MNRAS 380(3) 1079-1086

Image Virgo Consortium
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Aims and motivation

• How does dark energy affect the clustering of
  dark matter?
• Forthcoming surveys will measure structure to
  unprecedented precision
• Present theory cannot rapidly predict the effects
  of dark energy as accurately as they will be
  observed!

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Matter Power Spectrum

• Describes the clustering of matter on different
  scales
• Measurable by weak lensing and galaxy redshift
  surveys

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Matter Power Spectrum

• Describes the clustering of matter on different
  scales
• Measurable by weak lensing and galaxy redshift
  surveys

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Fluctuations grow under gravitational attraction
Gravity
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Fluctuations grow under gravitational attraction
Gravity
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Fluctuations grow under gravitational attraction

• Growth opposed by the expansion of the Universe

Expansion of the Universe
Gravity
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Fluctuations grow under gravitational attraction

• Growth opposed by the expansion of the Universe
• Since w(a) affects a(t), we get a different
  growth history

Expansion of the Universe
Gravity
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Dark energy and modified gravity

• Concordance cosmology means that probes of
  structure and probes of distance imply the same
  physics
• Assuming standard gravity we can reconstruct w(a)
  from structure data
• If w(a) from distance (Supernovae) and that from
  structure formation differ this is a clear sign
  of modified gravity

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Linear Growth Factor
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Matter Power Spectrum Estimation

• Most trusted current formula is known as Halofit
  (Smith et al 2003)
• Semi-analytic, simulation calibrated
• Valid only for w-1 (Cosmological Constant)

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Constant w correction

• McDonald et al (2006) computed corrections to
  Halofit for the power in w models relative to
  w-1
• Uses a grid of simulations fit to a
  multipolynomial fitting function

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A Simpler Way?

• Linder White (2005) found a method to match the
  non-linear growth to within 1 without a complex
  fitting formula
• Requires the matching of the linear growth today
  and at a high redshift point

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Distance to the LSS
Models with different w(a), but otherwise
identical cosmology that have the same distance
to the LSS are (nearly) degenerate with CMB
measurements This seems a natural place to look
for matching growth
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Distance to the LSS
Models with different w(a), but otherwise
identical cosmology that have the same distance
to the LSS are (nearly) degenerate with CMB
measurements This seems a natural place to look
for matching growth
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Matching Distance with w(a)

• w(a) w0 (1-a) wa

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Matching Distance with w(a)

• w(a) w0 (1-a) wa

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Linear Growth
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N-Body Simulations

• Used GADGET-2 N-Body code
• Main simulations used 2563 particles in a 256
  Mpc/h periodic box
• Other box size and particle number combinations
  used to check convergence

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A Very Good Match
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Why does distance matching work?

• By a simple numerical search involving a single
  differential equation we can match non-linear
  power to 1 relative accuracy
• What physical conditions allow this simple scheme
  to succeed?

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Crossovers
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Crossovers
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Crossovers
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Crossovers
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Crossovers
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Non-Linear Power
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Are these results real or numerical artifacts?
RMS errors roughly equal to difference between
models But can we reproduce this result with a
different realisation?
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Sampling Errors
Difference in power for a single model (w-1) in
different realisations of the initial density
field Variations of 10, much more than the 1
variation due to different w(a) models
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Ratio differences
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Ratio differences

• Despite the absolute power varying with
  realisation, the relative power between models
  does not vary

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Evolution of the Power Spectrum
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Evolution of the Power Spectrum
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Evolution of the Power Spectrum
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Evolution of the Power Spectrum
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Future Work

• Variations of other parameters to map w(a) model
  to any constant w
• Fitting formula for w(a), parameter independent
  (based on energy density?)
• Interacting models where dark energy and dark
  matter exchange energy