non-linear matter power spectrum to 1% accuracy between dynamical dark energy models matt francis...
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![Page 1: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649d235503460f949fa11f/html5/thumbnails/1.jpg)
Non-linear matter power spectrum to 1% accuracy between dynamical
dark energy models
Matt FrancisUniversity of Sydney
Geraint Lewis (University of Sydney)Eric Linder (Lawrence Berkeley National
Laboratory)
MNRAS 380(3) 1079-1086
Image: Virgo Consortium
![Page 2: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649d235503460f949fa11f/html5/thumbnails/2.jpg)
Aims and motivationHow 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 SpectrumDescribes the clustering of matter on different scales
Measurable by weak lensing and galaxy redshift surveys
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Matter Power SpectrumDescribes the clustering of matter on different scales
Measurable by weak lensing and galaxy redshift surveys
![Page 5: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)](https://reader034.vdocuments.us/reader034/viewer/2022042821/56649d235503460f949fa11f/html5/thumbnails/5.jpg)
Fluctuations grow under gravitational attraction
Gravity
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Fluctuations grow under gravitational attraction
Overdensity
Gravity
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Fluctuations grow under gravitational attraction
Growth opposed by the expansion of the Universe
Overdensity
GravityExpansion of
the Universe
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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
Overdensity
GravityExpansion of
the Universe
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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 correctionMcDonald 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
r
aa
a
a awwwmm eaa
da)1(3)1(33 0)1(
~Distance
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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
))(1(3 awH ww
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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