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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

Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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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)

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)

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!

Page 3: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Matter Power SpectrumDescribes the clustering of matter on different scales

Measurable by weak lensing and galaxy redshift surveys

Page 4: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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)

Fluctuations grow under gravitational attraction

Gravity

Page 6: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Fluctuations grow under gravitational attraction

Overdensity

Gravity

Page 7: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Fluctuations grow under gravitational attraction

Growth opposed by the expansion of the Universe

Overdensity

GravityExpansion of

the Universe

Page 8: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 9: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 10: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Linear Growth Factor

Page 11: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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)

Page 12: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 13: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 14: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 15: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 16: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Matching Distance with w(a)

w(a) = w0 + (1-a) wa

Page 17: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Matching Distance with w(a)

w(a) = w0 + (1-a) wa

Page 18: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Linear Growth

Page 19: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 20: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

A Very Good Match

Page 21: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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?

Page 22: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Crossovers

Page 23: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Crossovers

Page 24: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Crossovers

Page 25: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Crossovers

Page 26: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Crossovers

))(1(3 awH ww

Page 27: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Non-Linear Power

Page 28: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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?

Page 29: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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

Page 30: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Ratio differences

Page 31: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Ratio differences

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

Page 32: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Evolution of the Power Spectrum

Page 33: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Evolution of the Power Spectrum

Page 34: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Evolution of the Power Spectrum

Page 35: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

Evolution of the Power Spectrum

Page 36: Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis University of Sydney Geraint Lewis (University of Sydney)

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


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