Lecture 7:Our Universe
1.  Traditional Cosmological tests
– 
– 
– 
Theta-z
Galaxy counts
Tolman Surface Brightness test
2.  Modern tests
– 
– 
– 
– 
– 
HST Key Project (Ho)
Nucleosynthesis (Ωb)
BBN+Clusters (ΩM)
SN1a (ΩM & ΩΛ)
CMB (Ωk & ΩR)
3.  Latest parameters
4.  Advanced tests (conceptually)
– 
– 
CMB Anisotropies
Galaxy Power Spectrum
Course Text: Chapter 6 & 7
Wikipedia: Dark Energy, Cosmological constant, Age of Universe
Cosmological tests
•  The proper distance, dp, is the critical expression to test in
all experiments
– 
– 
– 
– 
Find a standard candle in luminosity or size.
Measure that quantity to a large redshift
Compare distance or angle and redshift to constrain Ωs
Tests geometry not dynamics
•  Typically we test either:
–  Angular size v distance, e.g., cluster size, radio lobes, CMB anisotropy
–  Luminosity v distance, e.g., SNIa, Bright Cluster Galaxies
–  Number-density v distance, e.g., Space-density of galaxies, galaxy counts
•  Above all test geometric effects not dynamics:
–  Test in planning with ELT which will look at dynamics (i.e., re-measure
redshift after a small time interval to measure change with time).
Theta-z
•  Assume radio lobes of radio galaxies are constant
in size.
–  Popular test in 1960-1980s
–  Provided first indication that model makes sense
–  Idea:
1
–  In a Euclidean Universe: ! !
d
Fixed Rod
θ
–  In a curved Universe: ! !
1
, d a = f (" M " R "k " # , z )
da
Fixed Rod
θ
Curvature
Theta-z relation
Radio lobe data
While demonstrating the effect expected the radio lobe data
was never accurate enough to distinguish between models.
Main concern was evolution of the radio lobes. However test was
reborn when CMB anisotropies were discovered.
Radio
Lobes
Quasar
Current Theta-z
•  Recent observations use compact radio sources
Galaxy Number Counts
•  In 1936 Hubble proposed using galaxy counts to
measure geometry
–  If galaxies uniformly distributed then expect differential number
v magnitude to be different.
–  200’’ telescope at Mt Palomar constructed
Number-counts per dm interval
FLAT CONTRACTING
EUCLIDEAN
OPEN EXPANDING
FLAT EXPANDING
CLOSED EXPANDING
Apparent magnitude
Volumes in expanding space
For very small triangle number of squares is roughly the same.
As the triangle grows the number of squares sampled becomes
noticeably different:
closed = increase in squares falls off
flat = squares increase linearly
open=squares increase faster than linear.
Galaxy counts
EUCLIDEAN
ΩM=1
ΩΛ=0
Galaxy Counts
Main problem
again evolution
(Tinsley et al)
Neuschaefer et al. G-Based
Casertano et al. HST(WF/PC)
Driver et al. HST(WFPC2)
Attempts made
to isolate elliptical
Galaxies which
should have least
evolution but then
Errors dominated
by ability to identify
Ellipticals.
Classification
uncertainty
Galaxy count work
no longer used for
Cosmology but to
study galaxy evolution
Fig. 2
Tolman SB test
•  Proposed in 1930s
•  In static Euclidean Universe SB is distance independent
•  In an expanding Universe it depends on the curvature
–  (1+z)-4 in a flat Universe
•  Results supported notion of
expansion but once again
test too crude for precision
cosmology
Classical tests
•  All three tests showed the general effect expected
–  Sizes fall more slowly than expected
–  Galaxy counts not linear but drop off
–  Surface brightness not distance independent
•  But all were plagued by evolution of the standard
candle
–  Radio lobes will evolve and grow with time
–  Galaxies evolve getting brighter/fainter/more numerous etc.
–  Because galaxies get brighter SB is also affected.
•  From 1980s the era of discovery cosmology began
powered by new facilities and supercomputers
•  By 2000 the Concordance Model emerged
•  But its an odd set of params. in many ways…
Big Bang Nucleosynthesis, Ωb
See Lecture 2.
Abundance measurements
of the light elements tightly
constrain the baryon
density.
Perhaps more importantly
the independent measures
of the different light
elements all concur.
Ho
!b h ~ 0.02, h =
100
!b ~ 0.04
2
BBN+Cluster M/L, ΩM
•  If clusters represent a fair sample of the Universe
one can derive their Dark-to-baryon mass ratio.
•  The idea is large bound structures will retain their
baryons and dark matter.
– 
– 
– 
– 
Motion of galaxies and/or lensing and/or SZ à DM mass
X-ray observations of inter-cluster gas à ionised mass
Optical census of cluster à stellar masses (very small)
Radio census of cluster à Neutral gas mass (very very small)
–  Typically:
!DM =
M DM
!b
Mb
!M = (
M DM
+1)!b
Mb
M DM
~5
Mb
!M ~ 0.25
Supernova Type Ia, ΩΛ
•  SNIa believed to be standard candles much like Cepheids
–  Caused by accretion onto a WD at a specific mass goes SN.
–  Happens at fixed mass è fixed luminosity à standard candle.
•  If we can measure peak brightness and the redshift we can use the
magnitude-distance relation to measure prams.
m = M + 5log10 [dl (z, H o , !M !"!K )]+ 25 + Av + K(z)
Apparent mag
(can measure)
Can derive from
Local SNIa spectra
z via redshift
Ho via Cepheids
Absolute mag
(calibrate locally)
Can estimate redenning
From colours
•  Only unknowns are: ΩMΩΛΩK but Ωk=0 from CMB
•  Just need to find SN and measure light curves
Nearby SN (Calibrator)
More distant SN
SNIa light
curve
SNIa do show some sign of
Variation, i.e., not perfect
Standard cnadles (top figure)
However brighter SNIa have
broader light curves (top figure)
Once this is taken into account
(bottom figure) SNIa look like an
ideal standard
candle
(Re)discovery of Λ
•  Two independent groups competing
–  High-z Supernova Search Team (Reiss et al 1998)
–  Supernova cosmology project (Perlmutter et al 1997)
–  Both report non-zero Λ
Alternative interpretations
•  Result is that galaxies appear fainter by ~20% over
expectation for an EdS Universe.
•  Could other effects cause this:
–  Dust attenuation:
–  Normal dust reddens light but spectra show no effect
–  Grey dust, e.g., large dust grains > wavelength
–  Unphysical
–  Evolution of SNI1, e.g., metallicity
–  Models show minimal effect
–  GR wrong/incomplete in some other way (e.g., Tired Light)
•  SN searches gave the first indication
•  CMB and LSS studies provided orthogonal support.
•  Increased age of Universe from 9Gyrs à 14Gyrs
–  More consistent with GC ages (~13Gyrs).
CMB, ΩR, ΩK
•  BB spectrum at z=0 gives ΩR precisely
8# h
"3
!" d" = 3
d"
c exp(h" / kBT ) !1
8# 5kB4 4
!16
4
!=
T
=
7.565
"10
(2.725)
15h 3c 3
!
$ R = 2 = 4.5 "10 !31 kgm !3
c
$R
#R =
~ 0.00002
$Crit
•  First anisotropy peak gives extreme theta-z test
–  The early Universe was lumpy (see next lecture on inflation)
–  Over-densities in the radiation field flow out dragging the
baryons with them at the sound speed.
CMB
•  The early Universe was lumpy (see next lecture on
inflation)
•  Over-densities in the radiation field flow out
dragging the baryons with them at the sound
speed.
Eqn of state for radiation
!1
$
d # c2 p&
d!
"3
% c
vs2 =
=
=
dp
dp
3
•  At decoupling baryons are left behind
ls = vs t =
ct
3
•  This gives an over-density on a particular scale.
ls =
ctdecoup
3
Temp. at which H atom kept ionised by BB photon distribution (nγ/nb)
(1+ z) =
Ro
Rdecoup
=
Tdecoup
To
=
3000
= 1111
2.7
Age at which decoupling occurred dictated only by Ho,ΩM because for
most of the time from BB to Decoup matter dominated.
1
tage =
!
0
$1
1
1
["M (1+ z) + " R (1+ z)2 + "# (1+ z)$2 + "k ] 2 d
Ho
(1+ z)
Evaluating using current params gives:
tdecoup ! 380, 000yrs
Valid for similar ΩM
3
Note:
" Rdecoup % 2
(3
2
[tdecoup,EdS = to $
[1+ z] 2 ! 230, 000yrs]
' =
3H o
# Ro &
CMB theta- test
•  BB predicts lumps on scales of 2ls~0.14Mpc at
decoupling (or 0.08Mpc for EdS)
•  Can measure anisotropies.
0.14Mpc
θ
da=f(z,ΩM,ΩR,ΩΛ)
! (!M = 1.00, !" = 0.00) = 0.50
da (!M = 1.00, !" = 0.00) = 9.3
da (!M = 0.25, !" = 0.00) = 27.3
da (!M = 0.25, !" = 0.75) = 13.2
$ ls '
! = 2 tan & )
% da (
#1
! (!M = 0.25, !" = 0.00) = 0.30
! (!M = 0.25, !" = 0.75) = 0.6 0
Peak~10
Results:
Assignment 2 & 3
•  Recent results from WMAP (see
http://letterstonature.wordpress.com/2010/01/29/wmap-7cosmological-parameter-set/), find:
T = 2.725K
H o = 70.2km/s/Mpc
!b = 0.0455
!dm = 0.227
!m = 0.272
!" = 0.728
zeq = 3196
to = 13.78Gyr
•  From these parameters derive:
i.  The density of radiation today in kg m-3
ii.  The redshift range over which matter dominates the dynamics
iii.  The temperature at matter-radiation equilibrium
iv.  The age of the Universe at matter-radiation equilibrium (use approximation)
v.  The temperature of the Universe 1s after the Big Bang
vi.  The radiation, mass, and vacuum densities 1s after the Big Bang (in kgm-3)
vii.  The proper distance to an object at z=1 (HINT: find an online cosmology
calculator)
viii. The apparent magnitude of a galaxy with M=-20 mag at z=1 (ignore dust
attenuation and the K-correction).
ix.  The apparent diameter of a galaxy in arc seconds assuming the galaxy’s
intrinsic radius is 15kpc.
x.  What is the minimum size an object 1kpc across can appear on the sky and
how does this compare to the resolution of the Hubble Space Telescope.
xi.  Finally relax and watch: http://www.vimeo.com/22956103 and then describe
what you find convincing and what you find unconvincing in the current
standard model.
• 
Tidy solutions with explanation as necessary to be handed in 11am
Friday 20th in person or via email.