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) Image: Virgo Consortium

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!

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

Matter Power Spectrum Describes 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 Gravity Expansion 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 Gravity Expansion 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 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

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

Matching Distance with w(a) w(a) = w 0 + (1-a) w a

Matching Distance with w(a) w(a) = w 0 + (1-a) w a

Linear Growth

N-Body Simulations Used GADGET-2 N-Body code Main simulations used 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

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

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

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