Non-linear matter power spectrum to 1% accuracy between dynamical dark energy models Matt Francis...

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

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!

Matter Power SpectrumDescribes the clustering of matter on different scales

Measurable by weak lensing and galaxy redshift surveys

Matter Power SpectrumDescribes the clustering of matter on different scales

Measurable by weak lensing and galaxy redshift surveys

Fluctuations grow under gravitational attraction

Gravity

Fluctuations grow under gravitational attraction

Overdensity

Gravity

Fluctuations grow under gravitational attraction

Growth opposed by the expansion of the Universe

Overdensity

GravityExpansion of

the Universe

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

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

Linear Growth Factor

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)

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

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

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

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

Matching Distance with w(a)

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

Matching Distance with w(a)

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

Linear Growth

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

A Very Good Match

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?

Crossovers

Crossovers

Crossovers

Crossovers

Crossovers

))(1(3 awH ww

Non-Linear Power

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?

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

Ratio differences

Ratio differences

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

Evolution of the Power Spectrum

Evolution of the Power Spectrum

Evolution of the Power Spectrum

Evolution of the Power Spectrum

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