1. 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

2. 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!

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

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

5. Fluctuations grow under gravitational attraction Gravity

6. Fluctuations grow under gravitational attraction Overdensity Gravity

7. Fluctuations grow under gravitational attraction Growth opposed by the expansion of the Universe Overdensity Gravity Expansion of the Universe

8. 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

9. 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

10. Linear Growth Factor

11. 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)

12. 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

13. 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

14. 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

15. 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

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

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

18. Linear Growth

19. N-Body Simulations Used GADGET-2 N-Body code Main simulations used 256 3 particles in a 256 Mpc/h periodic box Other box size and particle number combinations used to check convergence

20. A Very Good Match

21. 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?

22. Crossovers

27. Non-Linear Power

28. 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?

29. 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

30. Ratio differences

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

32. Evolution of the Power Spectrum

36. 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