The Baryon Acoustic Peak

1. The Baryon Acoustic Peak Nick Cowan UW Astronomy May 2005

2. Outline • Acoustic Peak • Statistical Methods • Results from SDSS • Summary

3. Acoustic Peak • Quantum fluctuations led to density variations in the early universe. • These density fluctuations generated sound waves. • Those sounds waves are responsible for the large-scale structure of the universe.

4. Density Fluctuations • Given an initial density fluctuation, how does it evolve? • Point-like pertubations are easy to follow. • An arbitrary density distribution can always be decomposed into point-pertubations. • Let’s look at point-pertubations!

5. Point-like Pertubation (r2) (comoving)

6. Plasma Sound Wave Sound wave propagates through plasma Dark Matter stays put Neutrinos stream off At the speed of light

7. Perturbation at Decoupling

8. Photons Break Free Photons stream off at speed of light

9. Intermission: Sound Speed Before recombination, have relativistic plasma After recombination, have baryonic gas

10. Sound Wave Stalls

11. Dark Matter and Baryons Flirt Baryons fall back into central potential DM falls into shell

12. Dark Matter and Baryons Merge Nowadays we expect baryons and DM to track each other.

13. Density Pertubation Today The central peak dominates because of CDM A faint shell due to the propagating sound wave should still be visible.

14. Statistical Methods • The specific density distribution of our universe is hard to obtain and contains loads of useless information. • The statistics of galaxy distribution should contain all the useful information.

15. Power Spectrum vs Correlation Function Fourier Transform Exact representation of density pertubations Correlation Function Contain all the useful information if fluctuations are isotropic. Power Spectrum Average over directions

16. 2-point Correlation Function

17. Correlation and Covariance Statistical Correlation Covariance Standard Deviation Where the Covariance Matrix is: and the variance is given by: The diagonal terms in the covariance matrix quantify the “shot noise”

18. Observations • Size matters. • Good redshifts don’t hurt, either. • SDSS provides the largest catalogue of spectroscopic galaxies. • Use Luminous Red Galaxies to get a (nearly) complete sample out to z=0.47 • SDSS is “more bulk than boundary”.

19. Flashback The central peak dominates because of CDM Correlation Function A faint shell due to the propagating sound wave should still be visible.

20. Results from SDSS Points look too high because the covariance is “soft” w.r.t. shifts in . Correlation Function for 46,748 LRGs Holy S**t! There’s the peak!

21. Systematics • Radial Selection: even if you ignore redshift data, still get a peak. • Selection of LRGs is sensitive to photmetric calibration of g,r and i bands. • Calibration errors in SDSS (along the scan direction) should not be important. • Different redshift slices all exhibit the acoustic peak. Low z High z Peak is still there!

22. Covariance Matrix • The covariance matrix is constructed from the sample of LRGs. • It shows considerable correlation between neighboring bins (off-diagonal terms) and an enhanced diagonal from shot noise. • 2 = 16.1/17 which is reasonable. • Check the matrix by comparing jack-knifed samples to each other. • Compare to a covariance matrix based on the Gaussian approximation. • Other fancy statistical tricks

23. Summary • Sound waves stall at recombination. • They should always be found the same distance from the central CDM peak. • We can still see the signature of these sound waves in the distribution of galaxies as a baryon acoustic peak. • The position and size of the peak is consistent with the WMAP cosmology.

24. References • Eisenstein et al, astro-ph/0501171 • Eisenstein, “What is the Acoustic Peak?” • Peacock, Cosmological Physics (1999) • Ryden, Introduction to Cosmology (2003)