Cosmology and Large Scale
Structure of Universe
PHZ 6607
Nimit Agarwal
Prof. Bernard Whiting
Outline
• Cosmological Probes and ΛCDM Model.
• Redshift Surveys as Large Scale structure
Observations.
• Statistical tools for analysis
• Results from Observations
•Redshift Distortions
•Correlation functions
•Baryonic Acoustic Oscillations
Cosmological Probes
• CMB → Geometry of Universe is Flat
universe
• Large Scale Matter Distribution → There is
less than critical density of matter.
• Distant supernovae → Expansion of
Universe is accelerating
ΛCDM Cosmological Model
• Flat Universe Ω=1
• Dark Energy: Λ cosmological constant for
expanding universe. ΩDE =.7
• Dark Matter-non relativistic non-interacting
ΩCDM =.22
Ωb =.04
• Six Cosmological parameters: H, Ωm , Ωb ,
Optical depth to reionization, scalar fluctuation
amplitude and scalar spectral index
Hubble Law
•
•
•
•
All galaxies are moving away from us.
Isotropic expansion of Universe.
Hubble law: v=H0 d at low redshift
Measuring z gives
d=cz/Ho
Redshift Surveys
A redshift survey of strip
of sky is a slice through
3D galaxy distribution
Redshift Surveys
2df Galaxy Redshift Survey contains 63,000 galaxies
Statistical tools
• Correlation function
P12=n2(1+ξ(r)) dV1dV2
• ξ(r) > 0:
more clustered than random
DD(r )
1
• ξ(r) =
RR(r )
Data-data pairs Random-random pairs
• Power spectrum
P( k )
ik .r
3
( r )e d r
Statistical tools
• Data points are in redshift space.
• Correlation function ξ(rp,π)
• Projected correlation function
lim it
p
(rp ) 2
(rp , )d
0
Cosmology by eye !
Redshift space distortions
Small scale
Fingers of God effect.
Large scale
Kaiser effect-Flattening
due to coherent infall.
Redshift Distortions
• Distortion parameter
β=Ωm / b = 47±.07
• δgalaxies = b δdark matter
• Ωm =.27
• Ωm =.3
for b=1
for b=1.2
Correlation Function
• Correlation decreases
with scale.
• Acoustic Peak at large
scale.
• Power law ξ(r)=(r/ro)-1.8
on small scales.
Correlation function
• Deviations on small
scales (r<10h-1 Mpc)
• Fitted to two power
functions- two clustering
regimes
• Small scales- from
same halo.
• Large scales- from
different halo.
Power spectrum
• Ω m ≠ 1 looking at the turnaround point.
• Ω m = .22±.04
Baryonic Acoustic Oscillations(BAO)
• Peak in ξ(r) at 100 h-1
Mpc
• Oscillations in P(k) (BAO)
• No peak for Ω b = 0.
Apeak α Ω b
• Small peak amplitude
from CMB--non photonbaryon interacting matter
CDM
Origin of BAO
Origin of BAO
Origin of BAO
Origin of BAO
Recombination takes place
Origin of BAO
Origin of BAO
Origin of BAO
BAO as “standard ruler”
• At particular redshift, it gives angular
distance.
• Hence Dθ(z)
Compare
Dθ(z1)/ Dθ(z2) from BAO
with
Dr(z1)/Dr(z2) from cosmological model
BAO as “standard ruler”
• For z1=.35 and z2=.2 ,
ratio from BAO=1.8
ratio from model(Ωm=.25)=1.67
not close
• May be inherent curvature or w(z)
Cosmology from CMB and
2dfGRS
Combining CMB and 2dfGRS reduces degeneracy and improves
constraints