1. Using Baryon Acoustic Oscillations to test Dark Energy Will Percival The University of Portsmouth (including work as part of 2dFGRS and SDSS collaborations)

2. Baryon Acoustic Oscillations “Wavelength” of baryonic acoustic oscillations is determined by the comoving sound horizon at recombination At early times can ignore dark energy, so comoving sound horizon is given by Sound speed c s varying the baryon fraction Gives the comoving sound horizon ~110h -1 Mpc, and BAO wavelength 0.06hMpc -1 Image credit: Martin White

3. BAO as a standard ruler If we are considering radial and angular directions using randomly placed galaxy pairs, we constrain (to 1st order) BAO position (in a redshift slice) therefore constrains some multiple of Varying r s /D V Changes in cosmological model alter measured BAO scale (∆d comov ) by: Radial direction (evolution of Universe) Angular direction (line of sight)

4. Extracting BAO from P(k) fit data with a 2-component model comprising a smooth spline (node separation 0.05hMpc -1 ), and the sinusoidal (in the transfer function) multiplicative BAO component usually applied to a CDM model. The ability of this model to fit linear CDM power spectra is good. Percival et al., 2007, astro-ph/0608635 & astro-ph/0705.3323

5. The SDSS DR5 sample Main sample galaxies Type-I LRGs Type-II LRGs After various selection cuts, the DR5 sample gives 51251 LRGs and 462791 main galaxies (factor ~2 larger than previously analysed)

6. BAO from all the SDSS DR5 galaxies Compared with WMAP 3-year best fit linear CDM cosmological model. N.B. not a fit to the data, but a prediction from WMAP. Interesting features: 1. 1.Overall P(k) shape 2. 2.Observed baryon acoustic oscillations (BAO) Percival et al., 2007, ApJ, 657, 645

7. Matter density from SDSS BAO When combined with, and marginalised over the WMAP 3-year peak position, For flat  CDM cosmologies Percival et al., 2007, ApJ, 657, 51

8. Comparing CMB & BAO SDSS GALAXIES CMB CREDIT: WMAP & SDSS websites

9. Comparing BAO at different redshifts CREDIT: WMAP & SDSS websites SDSS LRGs SDSS main galaxies + 2dFGRS Tell us more about the acceleration, rather than just that we need it! z=0.35z=0.2

10. Combining the SDSS and 2dFGRS Work for astro-ph/0705.3323 in collaboration with: Shaun Cole, Dan Eisenstein, Bob Nichol, John Peacock, Adrian Pope, Alex Szalay

11. BAO from the 2dFGRS + SDSS BAO detected at low redshift 0<z<0.3 (effective redshift 0.2) BAO detected at high redshift 0.15<z<0.5 (effective redshift 0.35) BAO from combined sample (detected over the whole redshift range 0<z<0.5) Percival et al., 2007, MNRAS, astro-ph/0705.3323

12. Galaxy distances needed for analysis Galaxy redshifts need to be converted to distances before BAO can be measured Not a problem for small numbers of parameters, but time consuming for more Solve problem by parameterizing distance- redshift relation by smooth fit with small number of modes: can then be used to constrain multiple sets of models For SDSS+2dFGRS analysis, choose two modes at z=0.2 and z=0.35, for fit to D V This forms an intermediate link between the cosmological models to be tested and data

13. BAO distance scale constraints Constraint from D V (0.35)/D V (0.2) Constraint fitting r s /D V (z) Constraint including observed peak distance constrain from CMB r s /d A (cmb)=0.0104 SCDM OCDM  CDM

14. Cosmological constraints Constraint from D V (0.35)/D V (0.2) Constraint fitting r s /D V Constraint including distance to CMB Consider two simple models: 1. 1.  CDM 2. 2. Flat, constant w

15. Cosmological constraints with SNLS   Consider two simple models: – –Lambda-CDM – –Flat, constant w

16. Discrepancy with  CDM? LRG BAO on too small scales: further away than expected, so more acceleration between z=0.2 and 0.35 Discrepancy is 2.4  Can increase BAO damping and reduce significance of result, but then match with data becomes worse

17. conclusions  BAO offer an attractive method for DE studies – Good reasons to believe that systematics are of low amplitude – Physics is well known and can be modeled today  SDSS+2dFGRS measures BAO and r s /D V at z=0.2, z=0.35 – Constraint D V (0.35)/D V (0.2) = 1.812 is higher than predicted by LambdaCDM+WMAP+SNLS D V (0.35)/D V (0.2) = 1.67 (2.4  discrepancy). Needs more acceleration at low redshift – But, can reduce significance slightly by adjusting BAO fit  Many future BAO experiments are planned – BOSS, DES, PanSTARRS, WFMOS, ADEPT, SPACE, HetDEX, SKA, …

18. Why BAO are a good ruler No change in position of oscillations, just a damping term. Suppose that we measure an observed power that is related to the linear power by (halo model) Linear baryon acoustic oscillations are ratio of linear matter power spectrum to a smooth fit Then observed oscillations are related to linear BAO by To change the observed positions of BAO, we need sharp features in the observed power Eisenstein, Seo & White 2006, astro-ph/0604361 Percival et al. 2007, astro-ph/0705.3323 Linear bias model also predicts this form For linear bias model, peculiar velocities of galaxies gives Gaussian damping with width ~10Mpc