1. Cosmological Constraints from Baryonic Acoustic Oscillations
Carlton Baugh
Institute for Computational Cosmology
Durham University
Unity of the Universe Portsmouth 30th June 2009

2. Outline: cosmology from BAO
BAO: the basics
BAO: in practice
Constraining dark energy: the next steps

3. BAO: the basics
(Wayne Hu)
(Daniel Eisenstein)
Oscillations in photon-baryon fluid: pressure vs gravitational instability
Sound wave propagates until decoupling of matter and radiation
Maximum wavelength is horizon scale at decoupling

4. The BAO signal RADIATION MATTER Divide matter spectrum by
First predicted by Peebles & Yu 1970, Zeldovich 1970
Clear peaks in radiation spectrum
Peaks out of phase between Cl and P(Kk)
Reduced amplitude in matter P(k)
BAO scale related to sound horizon at recombination
Considered as a standard ruler
RADIATION
MATTER
Divide matter spectrum by
Featureless reference to
Emphasize BAO signal
Meiksin, White & Peacock 1999

5. Relating BAO standard ruler to cosmological parameters
BAO scale is approx. Standard ruler
Radial measurement gives H(z)
Perpendicular measurement gives angular diameter distance
Sound horizon scale known from CMB
(David Schlegel)

6. Relating BAO to cosmological parameters
Sound horizon:
(Eisenstein & Hu 1998)
(baryon density)
(matter density)
Constrain : H(z) – expansion history – dark energy equation of state
angular diameter distance – dark energy eqn of state
matter density
baryon density

7. Detection of BAO Eisenstein et al 2005 47,000 SDSS LRGs 0.72 cubic Gpc
Constraint on spherically averaged BAO scale
Constrain distance parameter:
Angular
diameter
distance
Hubble
parameter

8. Detection of BAO Best fit Linear theory Convolved with Survey window
function
Cole et al dFGRS main galaxy sample

9. How well do we need to measure BAO?
Hold other cosmological parameters fixed
dw ~ 7 ds (z=3)
dw ~ 4 ds (z=1)
Dark energy equation of state
Angulo et al
distance scale measurement

10. How well do we need to measure BAO?
s/Da held fixed
dw ~ 2 ds (z=3, z=1)
Dark energy equation of state
Angulo et al
distance scale measurement

11. BAO data: recent snapshot
Percival et al 2007
Joint analysis of 2dFGRS, SDSS main, SDSS LRG
For a flat universe and constant w, using WMAP s and SNLS data:

12. BAO data: recent snapshot
Measurement of spherically averaged BAO constrains:
BAO data give:
BAO by themselves favoured w<-1
SNe data suggest distance ratio 2.6 sigma away from this.
Percival et al

13. Modelling the BAO signal
Proof of concept work used linear perturbation theory: Blake & Glazebrook 2003; Glazebrook & Blake 2005; Haiman & Hu 2003
Extended/Renormalised Perturbation theory: Smith et al; Komatsu et al.
Simulations: Seo & Eisenstein 2003, 2007, Huff et al.; Takahasi et al 2009; Smith et al 2007; Smith/Sheth/Scoccimarro

14. The evolution of BAO Dark matter Sample variance in 500/h Mpc box
galaxies
Springel et al. 2005

15. Baryonic Acoustic Simulations at the ICC BASICC
L = 1340/h Mpc V=2.4/h^3 Gpc^3
(20 x Millennium volume)
N=1448^3 (>3 billion particles)
Can resolve galactic haloes
130,000 hours CPU on Cosmology Machine
Combine with semi-analytical galaxy
formation model GALFORM
50 low-res BASICC runs for errors
(= 1000 Millenniums!)
Angulo et al. 2008

16. Combine with galaxy formation model
H-alpha emitters
z=1
H-band selection
Alvaro Orsi et al. 2009

17. Distortions to the BAO signal
Nonlinear growth of fluctuations
Angulo et al. 2008

18. Distortions to the BAO signal
Nonlinear growth of fluctuations
Redshift space distortions
Angulo et al. 2008

19. Distortions to the BAO signal
Remove asymptotic bias: Scale dependent halo bias
Angulo et al. 2008

20. Distortions to the BAO signal
Scale dependent galaxy bias
Angulo et al. 2008

21. Distortions to the BAO signal
Nonlinear growth of fluctuations
Redshift space distortions
Scale dependent halo and galaxy bias
Angulo et al. 2008

22. Extracting the BAO signal
Define reference
spectrum from
measurement
Percival et al 2007
Angulo et al 2008

23. An improved fitting method
Percival et al 2007:
Define reference
Spectrum from measured P(k)
“De-wiggle” linear theory model to damp
higher harmonic
oscillations
BLUE: Blake & Glazebrook
RED: linear theory, dewiggled

24. Extracting the BAO signal: systematic effects?
Unbiased measurement
Accuracy of distance scale measurement
Scatter from 50 LBASICC
runs: each one has
volume 2.4 /h^3 Gpc^3
Angulo et al. 2008
redshift

25. Are BAO really a standard ruler?
+/- 1%
Correlation function
is FT of P(k)
BAO do not have
constant wavelength
or amplitude, so do not
get a sharp feature
Peak position is not
equivalent to the sound
horizon scale
Need to model shape
of correlation function
on large scales
Sanchez et al. 2008
Sound
horizon
Peak
position
Standard
LCDM
No Silk
damping

26. Peak position is not sound horizon
Sound horizon scale
matter density
Sanchez et al 2008

27. Systematics in the correlation function
Different samples have
same shape of
correlation function:
Real vs Redshift space
No bias vs strong bias
Sanchez et al. 2008
Correlation function less sensitive to effects causing gradients in P(k)

28. BAO measurements: update
Cabre & Gaztanaga 2008
Analyse DR6 LRGs
1/h^3 Gpc^3
Also measurment of radial BAO Gaztanaga et al

29. Do BAO and SNe constraints agree?
Modelling peak in correlation function gives consistent results with SNe.
Sanchez et al. 2009
Equation of state parameter
matter density

30. Ongoing/Future BAO measurements
Spectroscopic: WiggleZ, FMOS, BOSS, HETDEX, LAMOST, Euclid (ESA), IDECs (NASA+ESA?)
Photometric: Pan-STARRs, DES, LSST
require ~ order magnitude more solid angle to be competitive with z-survey (Cai et al 2009)
New surveys will ultimately probe on the order of 100 /h^3 Gpc^3

31. The future for modelling
Simulate quintessence model
w = w0 + w1(1-a) is not accurate model
Jennings et al 2009
Equation of state parameter
Expansion factor

32. Simulating quintessence DE
Models have different expansion histories to LCDM
Structure grows at different rates
Models with appreciable DE at early times have different linear theory P(k)
Jennings et al 2009
Dark energy density parameter

33. Baryon acoustic oscillations
z=0
SUGRA
Stage I : SUGRA linear growth factor
Multiplicative factor f corrects the scatter of the measured power from the expected linear theory
Invisible Universe 2009
Elise Jennings

34. Baryon acoustic oscillations
z=0
SUGRA
Stage I : SUGRA linear growth factor
Stage II : SUGRA linear theory
Elise Jennings

35. Baryon acoustic oscillations
z=0
SUGRA
Stage I : SUGRA linear growth factor
Stage II : SUGRA linear theory
Stage III: SUGRA best fit parameters
5% shift in second peak
Elise Jennings

36. Baryon acoustic oscillations
z=3
Elise Jennings

37. Baryon acoustic oscillations
Z=0
z=0 AS
Stage I : AS linear growth factor
Elise Jennings

38. Baryon acoustic oscillations
z=0 AS
Stage I : AS linear growth factor
Stage II : AS linear theory
Shift in second peak using LCDM parameters
Sound horizon at lss
CDM rs = Mpc
Stage I: AS rs = 137.8Mpc
Elise Jennings

39. Baryon acoustic oscillations
z=0 AS
Stage I : AS linear growth factor
Stage II : AS linear theory
Stage III: AS best fit parameters
<1% shift in second peak compared to CDM
Sound horizon at lss
CDM rs = 146.8Mpc
Stage III: AS rs = 149.8Mpc
Elise Jennings

40. Baryon acoustic oscillations
z=3
Elise Jennings

41. The future for modelling
Hard to distinguish LCDM and AS model from BAO
Jennings et al 2009
Equation of state parameter
Expansion factor

42. Summary
Starting a new age of BAO: beyond the approximate standard ruler
BAO remove some of shape information in two-point correlation function
Use realistic modelling to generate templates for BAO features to constrain parameters
Current SNe and BAO results now consistent
May be impossible to distinguish some DE models
Need to refine simulations in two ways:
Larger volumes able to resolve galactic haloes
Simulate other DE scenarios