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

Outline Acoustic Peak Statistical Methods Results from SDSS Summary

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.

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!

Point-like Pertubation (comoving) (r 2  )

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

Perturbation at Decoupling

Photons Break Free Photons stream off at speed of light

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

Sound Wave Stalls

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

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

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

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.

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

2-point Correlation Function

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

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”.

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

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

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!

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

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.

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