Transcript Cosmological Constraints from Baryonic Acoustic Oscillations

Cosmological Constraints from
Baryonic Acoustic Oscillations
Carlton Baugh
Institute for Computational Cosmology
Durham University
Unity of the Universe Portsmouth 30th June 2009
Outline: cosmology from BAO
• BAO: the basics
• BAO: in practice
• Constraining dark energy: the next steps
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
The BAO signal
RADIATION
MATTER
Meiksin, White & Peacock 1999
•
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
Divide matter spectrum by
Featureless reference to
Emphasize BAO signal
Relating BAO standard ruler to
cosmological parameters
(David Schlegel)
• BAO scale is approx.
Standard ruler
• Radial measurement
gives H(z)
• Perpendicular
measurement gives
angular diameter
distance
• Sound horizon scale
known from CMB
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
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
Detection of BAO
Best fit
Linear theory
Convolved with
Survey window
function
Cole et al. 2005 2dFGRS main galaxy sample
How well do we need to measure
BAO?
Dark energy equation of state
• Hold other
cosmological
parameters fixed
• dw ~ 7 ds (z=3)
• dw ~ 4 ds (z=1)
distance scale measurement
Angulo et al . 2008
How well do we need to measure
BAO?
Dark energy equation of state
• s/Da held fixed
• dw ~ 2 ds (z=3, z=1)
distance scale measurement
Angulo et al . 2008
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:
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. 2007
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
The evolution of BAO
Dark matter
Sample variance
in 500/h Mpc box
galaxies
Springel et al. 2005
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
Combine with galaxy formation model
H-alpha emitters
z=1
Alvaro Orsi et al. 2009
H-band selection
Distortions to the BAO signal
• Nonlinear growth of
fluctuations
Angulo et al. 2008
Distortions to the BAO signal
• Nonlinear growth of
fluctuations
• Redshift space
distortions
Angulo et al. 2008
Distortions to the BAO signal
Remove asymptotic bias: Scale dependent halo bias
Angulo et al. 2008
Distortions to the BAO signal
Scale dependent galaxy bias
Angulo et al. 2008
Distortions to the BAO signal
• Nonlinear growth of
fluctuations
• Redshift space
distortions
• Scale dependent
halo and galaxy bias
Angulo et al. 2008
Extracting the BAO signal
Define reference
spectrum from
measurement
Percival et al 2007
Angulo et al 2008
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
Accuracy of distance scale measurement
Extracting the BAO signal: systematic
effects?
Unbiased measurement
Scatter from 50 LBASICC
runs: each one has
volume 2.4 /h^3 Gpc^3
Angulo et al. 2008
redshift
Are BAO really a standard ruler?
+/- 1%
Correlation function
is FT of P(k)
Peak
position
Standard
LCDM
No Silk
damping
Sound
horizon
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 scale
Peak position is not sound horizon
matter density
Sanchez et al 2008
Systematics in the correlation function
Different samples have
same shape of
correlation function:
Real vs Redshift space
No bias vs strong bias
Correlation function less
sensitive to effects
causing gradients in P(k)
Sanchez et al. 2008
BAO measurements: update
• Cabre &
Gaztanaga 2008
• Analyse DR6
LRGs
• 1/h^3 Gpc^3
• Also
measurment of
radial BAO
Gaztanaga et al
Do BAO and SNe constraints agree?
Equation of state parameter
• Modelling
peak in
correlation
function gives
consistent
results with
SNe.
• Sanchez et al.
2009
matter density
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
The future for modelling
Equation of state parameter
• Simulate
quintessence
model
• w = w0 +
w1(1-a) is not
accurate
model
• Jennings et al
2009
Expansion factor
Dark energy density parameter
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
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
z=0
SUGRA
Stage I : SUGRA linear
growth factor
Stage II : SUGRA linear
theory
Elise Jennings
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
z=3
Elise Jennings
Baryon acoustic oscillations
z=0
Z=0
AS
Stage I : AS linear growth
factor
Elise Jennings
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 = 146.28Mpc
Stage I: AS rs = 137.8Mpc
Elise Jennings
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
z=3
Elise Jennings
The future for modelling
Equation of state parameter
• Hard to
distinguish
LCDM and AS
model from
BAO
• Jennings et al
2009
Expansion factor
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