Cosmic Microwave Background Temperature Anisotropies as a Cosmological Tool - The cosmic microwave background provides a multitude of rich ...
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Cosmic Microwave Background Temperature Anisotropies as a Cosmological Tool The cosmic microwave background provides a multitude of rich constraints on the character of density perturbations and on the parameters that describe our Universe.
Overview n Overview of Cosmic Microwave Background n Physical Processes responsible for CMB Anisotropies n Current results and future goals 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 2
Relic Radiation Predicted
n 1940s: Gamow, Alpher & Herman
proposed all chemical elements
synthesized via nuclear reactions in
hot early universe “ylem”
n Predicted existence of cosmic
background radiation as bi-product of
the synthesis of all the chemical
elements in the hot, dense early
Universe
George Gamow (1904-1975)
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 3
Primordial Nucleosynthesis
n Nucleosynthesis occurred when the Universe was a few
minutes old, with characteristic temperatures of 100keV,
109K, z~108-109
n Outcome sensitive to baryon to photon ratio 3 minutes: nucleosynthesis
few months: thermalization
n Baryons can fuse at these energies
n Collisions or interactions with photons lead to fission
n At high densities and temperatures, the radiation is rapidly
thermalized, producing a Planck spectrum
2hν 3 1
I ν (T ) = 2 hν j = σT 4
c e BT −1
k
n Photon number density scales as T3, temperature scales as
T(z)=T0(1+z)
n Baryon to photon ratio is conserved except during periods where
particle annihilation or other processes are creating photons
n Baryogenesis phase is one such phase where the baryonic Hu & White 2004
matter and antimatter annihilated, leaving only 1 billionth of the
population remainingà baryon to photon ratio today is
Thermal History of the Universe
n Post inflation, the Universe is
a high kT thermal plasma of
photons, matter, and
antimatter cooling with the
expansion
Reheating
Inflation
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 5
Cosmic Background Radiation (CMB)
n Discovered serendipitously in 1964 by
Arno Penzias and Robert Wilson at
AT&T Bell Labs
n Microwave noise
n Peak emission near 2mm
n Isotropic
Penzias and Wilson
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 6
COBE Satellite
n COsmic Background Explorer
n Launched 1989
n FIRAS
n Far Infrared Absolute Spectrometer
n DMR
n Differential Microwave Radiometer
n DIRBE
n Diffuse Infrared Background
Experiment
http://lambda.gsfc.nasa.gov/product/cobe/
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 7
COBE Spectrum: Blackbody Emission
n FIRAS instrument measured GHz
CMB spectrum 12
200 400 600
10
n No measurable deviations from
Planck spectrum 8
error x50
n T=2.725 (0.002) K 6
Mather et al 1999
4
n Tightly constrains interactions 2
between radiation and matter 0
between nucleosynthesis and 5 10
frequency (cm-1 )
15 20
recombination and between
recombination and present day
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 8
Recombination
n The process of the ionized electron-proton plasma
transforming to a neutral hydrogen gas p+ + e− ↔ H + γ
n There is an energy bonus of 13.6eV in this transition, but
energetic photons and collisions can reionize H atoms
n Taking Maxwell-Boltzmann forms for the number ΔE 3
densities of electrons, protons and hydrogen we can n p ne −
k BT ⎛ meT ⎞ 2
write the dependence of this transition on the ∝e ⎜ ⎟
temperature nH ⎝ 2π ⎠
n where DE=mp+me-mH~13.6eV redshift z
104 103 102
1
Because the photon to baryon ratio is so high (~109)
xe ionization fraction
n
recombination does not occur as temperature drops 10-1
below 13.6eV (157,000K). Rather, it occurs at a much Saha
10-2
lower temperature of 0.3 eV (~3000 K).
2-level
0.0105 −0.028 10-3
⎛Ω h ⎞
2 ⎛ Ωb h ⎞
2
1+ zr ≈ 1089 ⎜ m ⎟ ⎜ ⎟ Hu 2005
⎝ 0.14 ⎠ ⎝ 0.024 ⎠ 10-4 10-3 10-2
scale factor a
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 9
Reionization
n Universe is reionized at some later time First detection of Gunn-Peterson Effect
(~109yr) with the formation of the first
collapsed structures (massive star clusters,
low mass galaxies) through the prodigious
amounts of radiation produced by these
sources
n Appropriately energetic radiation (i.e. 13.6
eV) passing through neutral hydrogen is
easily absorbed, leaving clear evidence of
its presence
from Xiaohui Fan
n Evidence shown in quasar at z=6.28, so
there was sizeable neutral fraction (~10-3)
at that time
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 10SDSS Quasar Spectra 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 11
Probing the Surface of Last Scatter
n The observed cosmic microwave background on the sky is reflecting the
properties of the photons as they last interacted with matter at
recombination together with changes due to gravitational redshifting and
scattering as they travel through the Universe toward us
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 12COBE DMR: Dipole Temperature Variation
3.5x10-3 K warmer
3.5x10-3 K cooler
Origin: Doppler shift due to Solar System’s motion through space
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 13COBE DMR: Universe through Our Galaxy
Synchrotron emission from the galactic plane
dominates the emission at some frequencies
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 14COBE: Temperature Map of the Cosmos
n After subtracting dipole temperature variation and the
emission from the Milky Way, one finds…….
ΔTCBR ≈ (30 ± 5) ×10 −6 K Smoot et al 1992
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 15Significance of COBE Results
n Blackbody spectrum the most precise ever measured
n Confirms Universe began hot and in thermal equilibrium
n CMB intensity isotropic to few parts in 105
n Consistent with cosmological principle (homogeneity, isotropy)
n CMB anisotropies detected
n Implies small temperature and density variations in young universe
n Density fluctuations become galaxies, clusters of galaxies, large scale
structure later on
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 16Interpretation of the CMB Anisotropy 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 17
Anisotropies in the
CMB can also be
caused by effects
along the line-of-
sight to the observer.
Original anisotropies
in the CMB from the
Last scattering surface
astro-ph 0309240
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 18The following physical processes are responsible for the origin of CMB temperature
fluctuations in the last scattering surface:
On large angular scales (θ ~ 10°) the dominant source of fluctuations in the CMB photons
is the gravitational Sachs–Wolfe (SW) effect, simply describing the fact that photons gain
(or lose) energy when they escape from under-dense (or over-dense) regions (gravitational
redshift):
!" !Φ
= &
" %
On intermediate scales (θ ~ 1°, about 240 Mpc comoving distance) the baryonic
perturbations termed acoustic oscillations, which can be observed as acoustic peaks in the
angular spectrum of CMB fluctuations:
dT 1 dr B
= adiabatic + '( ~" * in BB
T 3 re, B
!
n
Small velocities DV in the last scattering surface cause Doppler-perturbations ( = line-
of-sight unit vector):
δT δV in
=
T c
On small angular scales (θ < 1°) the oscillations are damped, mainly by the process
called Silk damping (photon diffusion suppresses amplitude of small-scale perturbations).
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 19Spherical Harmonics and the Angular
Power Spectrum
n We have a temperature field on the
curved sky. T ( n̂ ) − T
n Convenient to transform to temperature Θ ( n̂ ) =
T
anisotropy
And expand using spherical harmonics,
n
Θ ( n̂ ) = ∑ ΘℓmYℓm ( n̂ )
which is an orthonormal basis on the
ℓm
surface of a sphere (sky)
n Second moment of temperature Θℓm * Θℓ'm' = δℓℓ'δmm'Cℓ
anisotropy is power spectrum
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 20Low order spherical harmonics
n Ylm (q,f) similar to Fourier
expansion but defined on the
curved surface of a sphere
n Ylm (q,f)=N eimf Plm(cos q)
n Where Plm(x) are the Legendre
polynomials and where –lWMAP CMB Example
n As with 3D P(k), the
angular power
spectrum Cl contains a
complete statistical
description of a
Gaussian field on the
sphere
l(l+1)Cl /2π (μK)2
n Cl is dimensionless, but
often shown with units
Squ(T) by multiplying
through by square of
mean temperature
l
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 22Connections between 2D and 3D Structure
n The sky map of the CMB
represents the (redshifted)
temperature of the photons that are
arriving from the surface of last
scattering
n If recombination took place in an observer
instant then we would be observing
temperatures on a vanishing thin n
D*
slice of angular diameter distance
dc(z=1089)
! recombination
Θ ( n̂ ) = ∫ dD Θ ( x ) δ ( D − Dr )
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 23Relationship between Angular and Spatial
Anisotropy Power Spectra
The spatial (3D) anisotropy can be expressed as ! d 3k ! ik⋅! x!
n
the Fourier transform of its transform pair
Θ( x) = ∫
( 2π )
3 ()
Θ k e
Then, as we saw with the density field before, we ! * ! ! ! !
n
can write the power spectrum of the anisotropy as () ( )
Θ k Θ kʹ = δ k − kʹ P(k ) ( )
n Defining the anisotropy variance per logarithmic k k 3 P(k)
2
interval as Δ (k ) =
T
2π 2
2π
it can be shown that (see Hu or Challinor reviews) Cℓ ≈
ℓ ( ℓ +1)
Δ T2 ℓ
Dr ( )
n l(l+1)Cl is Squ(DT) at k=l/Dr ℓ ( ℓ +1) Cℓ 2 2
2
Characteristics of 2D field tell us directly about 3D parent field.
Typically we will see: preference for units of Squ(T) 2π
( T ) ≈ Δ T (T )
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 24Now on to the Spatial Temperature Field in
the Universe at Recombination
n Thomson scattering couples the photons and electrons
and Coulomb interactions couple the electrons and
baryons.
n The effectiveness of the coupling can be characterized
by the mean free path l between Thomson scatter
−1
events
n Two body scattering suggests the form
(λ ) = neσ T
n At recombination l~2.5MpcToward Acoustic Oscillations
n Following Hu, consider perturbations in the photon density field dng alone
n For the moment set aside Gravity (assuming radiation pressure dominates)
n As a Planckian spectrum ng=T3, so we can write
δ nγ δT
= 3 γ = 3Θ
nγ Tγ
n The density perturbations of photons are directly reflected in the temperature
perturbations… and the baryons are coupled to photons (DM is different)
n Note that expansion does not impact the fractional temperature
fluctuations.
n Thus, a measure of the temperature angular power spectrum is directly
connected to underlying 3D density power spectrum at recombination
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 26Evolution of Temperature Perturbations
n With no gravity, we have two governing equations
n Continuity equation
n Where vg is the photon fluid bulk velocity and we linearize
∂ ⎛ δ nγ ⎞ ! 1
⎜⎜ ⎟⎟ = −∇ ⋅ vγ Θ = − ∇ ⋅ vγ
∂t ⎝ nγ ⎠ 3
n Euler equation
n Through similar process of linearization can be written
v!γ = −∇Θ see S3.2 in Hu notes
n Combining one gets simple harmonic oscillator equation
From Lecture 2
!! + c 2 k 2Θ = 0
Θ a˙ & c 2k 2 )
δ˙˙ + 2 δ˙ = δ ( 4 πGρo − s 2 +
s
a ' a *
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 27Temperature Fluctuation Solutions
n Solutions can be written in the form
! (t )
Θ o
Θ (t ) = Θ (t0 ) cos ( ks ) + sin ( ks )
kcs
t
n Where s is the sound horizon s (t ) = ∫ dtʹ c s
to
n The first term is a perturbation with initial temperature amplitude and second
term is a perturbation with initial bulk flow velocity vg
n The sound horizon is always increasing.
n Depending on their wavelength l=2p/k, these perturbations are in a different
phases
n At recombination, amplitude modes with ksr=2pn will be at maximum,
ksr=(2n+1)p will be at minimum, and modes with ksr=(2n+1)p/2 will be at
null
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 28Adiabatic Perturbations and Acoustic Peaks
n These begin with finite temperature or density fluctuation with vanishing velocity
component
Θ (t ) = Θ (t0 ) cos ( ks )
n These all evolve together in time from some initial to.
n The power spectrum is related to the square of the temperature field, and therefore modes at
extrema of their values (ks=np) contribute equally whether positive or negative
n The fundamental physical scale is the sound horizon at recombination
π sr
kr = λr =
sr π
n Expect a series of peaks in the power spectrum in case of adiabatic
perturbations with l=lr/n and n=1, 2, 3 …
n Fundamental physical scale in 3D power spectrum is observed on the sky with
angular scale and depends on the angular diameter distance to the surface of
last scattering
λr
θr = ℓ r = kr d A ( zr )
d A ( zr )
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 29Expected peaks are observed
n Here l=p/q, and so the sequence of expected extrema at
l=lr/n and n=1, 2, 3 … show up at wavenumber lr, 2lr, 3lr,
…
l(l+1)Cl /2π (μK)2
l
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 30Taking stock: Cosmological Sensitivities
n So far, we have demonstrated that the CMB anisotropy angular power
spectrum reflects
n Scale of sound horizon at recombination sr
n Distance to surface of last scattering dA(zr)
n Sound horizon impacted by age of Universe at recombination, so the
expansion history in early Universe
n Radiation domination epoch and beginning of matter domination epoch
n rm=Wmh2, rr from CMB directly
n Baryon density- otherwise no acoustic oscillations rB=WBh2
n Angular diameter distance sensitive to expansion history in late
Universe
n Matter and dark energy domination phases Wm, WE
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 31From Surface of Last Scattering to
Observer
n Following Challinor & Peiris, we 2 2 ⎡ 2 !2 ⎤
ds = a (η )⎣(1+ 2ψ ) dη − (1− 2φ ) dx ⎦
adopt the conformal Newtonian
gauge
n h is the conformal time
dt
n f and y are scalar potentials. In dη =
absence of anisotropic stress f=y a
n Testing equivalence of these
potentials is of interest for testing
modified gravity models
n Various components affect evolution of density/temperature
perturbations on their way toward us
n Gravity
n Scattering
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 32Impacts of Gravity
n Gravity impacts the temperature perturbations dΘ ∂ψ ! !
as reflected by the free streaming photons in =− +φ +ψ
dη grav ∂η
several ways
n Gravitational redshifting of photons due to difference
of the potential well depth at the moment of
recombination hr and at the moment of observation see S2.3 Challinor Notes
hobs. This is the Sachs-Wolfe effect
n Time rate of change of the gravitational potentials ηobs
through which the photons pass introduce further
changes. This is the integrated Sachs-Wolfe effect Θ ISW = ∫ dη (φ! + ψ! )
(ISW) ηr
n ISW is split into early and late phases, with former
corresponding to end of transition from radiation to
matter domination and the latter corresponding to the era
of dark energy domination
n Gravitational lensing affects direction of photons–
typical CMB photon has been scattered by ~2 arcmin
relative to its direction at recombination
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 33Impacts of Scattering
n Thomson scattering can occur if there are enough free
electrons (before recombination and after reionization)
n 1st term- scattering out of beam dΘ ! !
2nd term- scattering into beam
≈ −ane T (
σ Θ − Θ o − e ⋅ vb )
n
dη scat
n 3rd term- Doppler effect due to moving electrons
see S2.4 Challinor Notes
n For isotropic photon distribution and electrons at rest the
scattering effect vanishes
n Scatter prior to recombination leaves imprint of velocities
associated with acoustic oscillations
n Scatter “within” the surface of last scattering also leads to photon
diffusion that suppresses perturbation amplitudes on small scales
n Secondary anisotropy like the kinetic and thermal Sunyaev-
Zel’dovich effects (SZE) provides useful probes of structure
formation
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 34Relative Importance of Different Effects
ηobs
n Overall combination ! ! !
⎡⎣Θ ( e ) + ψ ⎤⎦ = Θo + ψr + e ⋅ vb + ∫ dη (φ! + ψ! )
n 1st term is temperature of obs r r
ηr
CMB in direction e
n 2nd: yr-yobs gives
gravitational redshift
n 3rd: Doppler effect from
scattering of moving
electrons
n 4th: Integrated Sachs-
Wolfe when potentials are
evolving
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 35Universe Just Before Recombination
n Dark matter dominated, with tiny perturbations in the dark
matter growing
n Photons, protons and electrons are coupled through
electromagnetic scattering interactions
n Referred to as the photon-baryon fluid
n Exhibits pressure within causal region- the sound horizon
n The observable universe has a particular size at that
epoch (we now know this size spans 1 degree on the sky
in an image of the CMB)
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 36Oscillations in the Photon-Baryon Fluid
n Acoustic oscillations or standing waves are common on scales below the
sound horizon
n Oscillations have wavelengths that reflect the horizon scale as well as higher
harmonics that appear at smaller and smaller wavelengths
n The scale of the horizon is determined by the expansion history of the universe,
which determines also the age of the universe and the time a sound wave has
had to travel since the beginning
n The expansion history is very sensitive to the density of matter and radiation that
has led to deceleration of the universal expansion since the beginning of the
universe
n Thus, a measure of the wavelength of temperature variations in the CMB
provides a measure of the sound horizon, which in turn tells us about the amount
of matter in the universe
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 37Formal Solution
n Solving the full Boltzmann equation for the evolution of scalar and tensor
perturbations in the coupled components (baryons, dark matter,
neutrinos, radiation) is complex
n Work by Wayne Hu and Naoshi Sugiyama focused on formal solution
and the development of fitting formulae to elucidate the primary physical
dependencies
n Publicly available codes are commonly used to explore impact of a wide
range of parameters on Cl’s as well as P(k,z), the matter power spectrum
n CMBFast – Seljak and Zaldarriaga
n CAMB – Anthony Lewis
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 38Geometry and the Sound Horizon
n When we look at the CMB we
are seeing the apparent (i.e.
angular) size of the sound
horizon. Thus, we are not just
sensitive to the physical size of
the horizon-- but we are also
sensitive to the different paths
light takes in open and flat
geometries
n In hyperbolic geometry of an
open universe, an object of a
given intrinsic size at some
distance appears to be smaller
when viewed on the sky
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 39Open Versus Flat Geometry
n Geometry of the universe affects
the apparent scale of the typical
structures in the CMB
n The location of the first peak in
the CMB fluctuation spectrum is
very sensitive to the total density
parameter Wtot
n As Wm drops WE rises
n dA(zr) increases
n But so does sr
n Angular size almost unchanged
ΔT
(θ, φ ) = ∑ ΘlmYlm (θ, φ )
T lm
2
Cl ≡ Θlm
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 40Baryon Density
n Increasing the baryon
density is adding mass to
the photon-baryon
oscillations
n Increased mass
strengthens the
compressions and
weakens the rarefactions
n Ratio of peak heights
constrains this parameter
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 41Effects of Dark Energy
n Dark Energy has only modest
effects on the CMB
n On large scales the presence
of dark energy affects the
evolution of large scale
density perturbations that the
CMB photons travel through
after recombination
n Studies of dark energy of
cosmic acceleration focus on
structure formation tests and
distance measurements
rather than CMB
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 42Current Constraints and Future Goals 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 43
Constraints on CMB Fluctuations from the
Previous Century
n As recently as 1999 the Increasing scale
Typical Amplitude
observations of the CMB
anisotropy were not very
constraining
n Detailed statistical analysis of
the data suggested that a flat
universe was preferred, but as
is clear from this figure, the
case was less than convincing.
ΔT
(θ, φ ) = ∑ΘlmYlm (θ, φ )
T lm
2
Cl ≡ Θlm
Figure from Wayne Hu
Cosmology and Large Scale Structure - Mohr -
14. May 2021 Lecture 3 44BOOMERANG Flight
in 1998
Data of much higher
quality were already
on the way…
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 45BOOMERANG CMB Map with 1/6 degree resolution 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 46
The Spectrum of CMB Anisotropy
Flat model preferred
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 47Measuring Geometry with BOOMERANG
n Angular scale of typical
temperature fluctuation in
the CMB strongly indicates
a geometrically flat
universe
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 48BOOMERANG Maps of the CMB
de Bernardis et al. Nature 2001
Maps created in three of the BOOMERANG Channels
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 49Removing
Foreground
Emission
n Mapping in four
channels
1. 90GHz
2. 150 GHz
3. 240 GHz
4. 400 GHz
n Allows removal of
dust emission, bright
radio point sources
and synchrotron
emission from our
own galaxy
de Bernardis et al. Nature 2001
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 50DASI – Interferometer at
South Pole
n Interferometers measure the
Fourier transform of the
brightness distribution directly.
So they are well suited for
CMB anisotropy studies
n DASI was deployed in 2000 at
the South Pole for this purpose
by the Carlstrom team
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 51The Spectrum of CMB Anisotropy from DASI, an
Interferometer Operating from the South Pole
DASI provides
constraints on geometry
that are fully consistent
with those from
BOOMERANG
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 52Wilkinson Microwave Anisotropy Probe (WMAP)
= MAP observes the cosmic
microwave background through
10 differential microwave
radiometers, operating at 5
frequencies
= 22GHz
= 30GHz
= 40GHz
= 60GHz
= 90GHz
= Imaging the entire sky with 1/3
degree resolution to
unprecedented depth
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 53“In Search of a Quiet Place to do Science”
n WMAP satellite is currently
operating at L2, a so-
called Lagrange point.
This location is an
unstable point in space
formed by the gravitational
distortions from the Earth
and the Sun
n Minimizes interference
From MAP homepage
from the bright Earth and
Sun
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 54Wilkinson Microwave Anisotropy Probe
n WMAP has been in space since June 2001
(see http://wmap.gsfc.nasa.gov)
n 13 arcminute FWHM angular resolution (primary 1.4m x 1.6m)
n 45 times COBE sensitivity
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 55WMAP Resolution
n COBE mapped the
sky with 7 degree
resolution
n WMAP mapped the
sky with 1/3 degree
COBE image of the CMB
resolution
n In a flat universe the
sound horizon has
an apparent size of 1
degree, making sub-
degree resolution
critical in CMB
anisotropy studies
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 56
Simulated MAP image of the CMBWMAP Image of CMB 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 57
CMB Anisotropy WMAP+ACBAR+QUAD
Komatsu et al 2011
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 58WMAP 7th Year Cosmological Parameter
Measurements (Komatsu et al 2009)
n WMAP data brought us into a new era of Includes WMAP+SN H0 + BAO
precision cosmology
n Percent level constraints on fundamental Parameter Value
parameters
Combinations of datasets to break parameter
n
degeneracies H0 70.2+/-1.4 km/s
Ω k (95%) -0.0178 to 0.0063
n Other implications:
n Age is 13.76 +/- 0.11 Gyr Ω dm 0.229+/-0.015
n Reionization occurred at z=10.6+/-1.2
n Normalization of density fluctuation power Ω de 0.731+/-0.015
spectrum in the local universe is s8=0.816+/-0.024
n Sum of masses of neutrino species isArcminute Resolution CMB Mapping Experiments
n Atacama Cosmology Telescope (ACT)- 6m w/103 bolometers, 3-4
freq
n Led by Lyman Page, first light in 2008
n South Pole Telescope (SPT)- 10m w/103 bolometers, 3-4 freq
n Led by John Carlstrom, first light on Feb 16, 2007
n These are ideal for studies of secondary anisotropy, which dominates the sky at
small angular scales of an arcminute (1/60th of a degree)
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 60High Resolution Maps Offer New Information
n SPT maps offer smaller scale information to compliment WMAP
Keisler et al 2011
236 deg2
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 61Small Angular Scale Anisotropy
n Small scale anisotropy is more
complicated to interpret
n Power is contributed from other Keisler et al 2011
sources, including radio galaxies
and galaxy clusters, and this signal
becomes important relative to the
primary anisotropy above l~2000
(corresponding to ~5 arcmin scales)
SPT: 792 deg2
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 62Overview of WMAP+SPT Results (1)
n The wider range of l coverage leads to improved constraints on the
initial power spectrum of density perturbations
n Possible to constrain best value ns and first derivative simultaneously
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 63Overview of WMAP+SPT Results (2)
n The number of relativistic species
can be constrained through their
impact on the expansion history
during the radiation dominated era.
With WMAP parameters WB, the
sound horizon and era of matter-
radiation equality held fixed, the
main impact of increasing Neff is to
increase photon diffusion and
descrease small scale anisotropy.
So WMAP+SPT is much more
constraining than WMAP alone
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 64Planck Mission
n Planck launched in 2009
n 1.9m x 1.5m primary
n Factor of three higher angular
resolution than WMAP
n Much more sensitive
n Extends to higher frequencies
n Planck is also mapping at a larger range of
frequencies
1. 30 GHz
2. 44 GHz
3. 70 GHz
4. 100 GHz
5. 143 GHz
6. 217 GHz
7. 353 GHz
8. 545 GHz
9. 857 GHz
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 65Planck Pseudo-color Image of mm-wave Sky 14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 66
Predicted Constraints From MAP and Planck
Increasing scale
Planck Collaboration: Cosmological parameters
Typical Amplitude
n MAP and Planck will both
map the entire sky
6000
5000
n Planck resolution is better:
~1/6 degree resolution 4000 Planck XII (2015)
DT T [µK2 ]
3000
n Planck is also mapping at a
2000
larger range of frequencies
1. 30 GHz 1000
2. 44 GHz
0
3. 70 GHz 600 60
300
4. 100 GHz 30
DT T
0 0
5. 143 GHz -300 -30
6. 217 GHz -600 -60
2 10 30 500 1000 1500 2000 2500
7. 353 GHz
8. 545 GHz
9. 857 GHz Fig. 1. The Planck 2015 temperature power spectrum. At multipoles ` 30 we show the maximum likelihood frequency averaged
temperature spectrum computed from the Plik cross-half-mission likelihood with foreground and other nuisance parameters deter-
mined from the MCMC analysis of the base ⇤CDM cosmology. FigureInfrom
the multipole
WaynerangeHu2 ` 29, we plot the power spectrum
estimates from the Commander component-separation algorithm computed over 94% of the sky. The best-fit base ⇤CDM theoretical
14. May 2021 Cosmology
spectrum fittedand
to theLarge
Planck Scale
TT+lowPStructure
likelihood is-plotted
Mohrin-the
Lecture 3 Residuals with respect to this model67are shown in
upper panel.
the lower panel. The error bars show ±1 uncertainties.Planck 2016 Cosmological Parameter
Constraints- Spectacular!
n Planck measurements go beyond what Temperature, Polarization, Lensing
was possible with WMAP
Parameter Value
n Other implications: H0 67.48+/-0.98 km/s
Age is 13.799 +/- 0.021 Gyr
Ω k (95%)Planck Primordial Non-Gaussianity
Constraints
n Some models of inflation predict significant non-Gaussianity in the primordial
fluctuation spectrum Enhanced overdensity
2
Φ NG ( x ) = φ ( x ) + f NL (φ ( x ) − φ )
2
δ NG ≈ δ + 2 f NLφ p fNL>0
n As modes grow in the linear regime, the shape of the distribution of fluctuations is
preserved, but the amplitude grows. As evolution continues non-Gaussian
character also grows
n CMB anisotropy constrains directly the density perturbations in the linear regime
at the time of recombination
n Analysis of the CMB anisotropy bispectrum (3 point function) in Planck yields
precise constraints (Planck-24, 2014)
n Constraints on primordial non-Gaussianity consistent with Gaussian initial perturbation spectrum
local equil ortho
f NL = 2.7 ± 5.8 f NL = −42 ± 75 f NL = 25 ± 39
Local= squeezed triangles (s1Planck Constraints on Curvature
Fluctuations
n CMB anisotropy power spectrum provides constraints on
the type of underlying fluctuations, too
n Maximum allowed fraction of curvature fluctuation
contributions is 0.25%
n Planck paper 22 (2014)
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 70CMB Polarization Anisotropy
n Another important handle on state of the early Universe is through
the polarization signature
n One measures the CMB intensity for each mode of polarization and
examines the power spectrum
n E mode polarization is expected to arise from scattering
processes at recombination
n First detected by DASI experiment in 2002, studied in detail by Planck
n B mode polarization is expected to arise from gravitational
waves (i.e. tensor perturbations) introduced by Inflation.
n Detected in 2014 (BICEP), but non-cosmological (Planck 2015)
n New missions under development to address this question
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 71Planck Collaboration: The cosmological legacy of Planck
Planck Sky Maps
also in Polarization
n Full mission
Temperature (above)
and Polarization maps
(below)
n Polarization angular
power spectrum is
studied now in detail
n Typical E-E, B-B
0.41 µK -160 160 µK
Planck 2018: astro-ph/1807.06205v2
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 72Planck 2018:
Planck Collaboration: astro-ph/1807.06205v2
The cosmological legacy of Planck
CMB Anisotropy 6000
5000
Power Spectra
4000
D T T [µK2 ]
3000
2000
1000
0
n Shown are four power spectrum TT, 2 10 100 500
Multipole
1000 1500 2000 2500
TE, EE and the lensing potential 100
50
Best fit model to TT, TE and EE shown
D T E [µK2 ]
n 0
in all panels
50
100
n TT is sampling variance dominated at l 2 10 100 500
Multipole
1000 1500 2000 2500Planck 2018: astro-ph/1807.06205v2
Planck Collaboration: The cosmological legacy of Planck
B-mode Polarization Anisotropy: 90 1
Angular scale
0.2 0.1 0.05
the Next Frontier 103
CMB- TT
Planck
n B-mode polarization can be sourced by 102
WMAP
ACT
SPT
gravitational waves during the inflationary ACTPol
SPTpol
POLARBEAR
epoch. . The ratio of the amplitudes of tensor
BICEP2/Keck
BICEP2/Keck/
101
WMAP/Planck
and scalar modes in the CMB polarization is
D [µK2]
CMB- EE
linked to the energy scale of inflation 100
n Rescattering of B modes at recombination and 10 1
reionization lead to angular peaks (bumps) that
can help identify cosmological B-mode in the 10 2 CMB- BB
the next frontier
presence of foregrounds 3
10
n Now clear that foregrounds dominate the inflationary signal 100
Theforegrounds
B-Bump using
DTE [µK2]
n Special techniques of removing 0
primarily CMB• lensing information
Rescattering of gravitational should allowgenerates
wave anisotropy futurethe B-bump 100
missions to make this measurement
• Potentially the most sensitive probe of inflationary energy scale 200
107[ ( + 1)]2C /2
1.5
10 1.0
0.5
0.0
EE 0.5
∆P (µK)
2 150 500 1000 2000 3000 4000
Multipole
From Wayne Hu-
1
BB Fig. 18. Compilation of recent CMB angular power spectrum measurements from which most cosmological inferences are drawn.
The upper panel shows the power spectra of the temperature and E-mode and B-mode polarization signals, the next panel the
Beyond Einstein maximum
reionization
B-bump
recombination
B-peak
lensing
contaminant
cross-correlation spectrum between T and E, while the lower panel shows the lensing deflection power spectrum. Di↵erent colours
correspond to di↵erent experiments, each retaining its original binning. For Planck, ACTPol, and SPTpol, the EE points with large
error bars are not plotted (to avoid clutter). The dashed line shows the best-fit ⇤CDM model to the Planck temperature, polarization,
and lensing data. See text for details and references.
amplitude!
10 100 1000
l 27
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 74Planck 2018: astro-ph/1807.06205v2
Present epoch density power
Planck Collaboration: The cosmological legacy of Planck
spectrum
n A return to the Tegmark plot
showing different observational
constraints in the power
spectrum of density fluctuations
is instructive
n Constraints
n CMB anisotropy from Planck
n Cosmic Shear from DES
n Galaxy Cluster from SDSS
n Lyman alpha from BOSS
n Paints a picture of remarkable
consistency check of LCMD
model Fig. 19. Linear-theory matter power spectrum (at z = 0) inferred from di↵erent cosmological probes (the dotted line shows the
impact of non-linear clustering at z = 0). The broad agreement of the model (black line) with such a disparate compilation of
data, spanning 14 Gyr in time and three decades in scale, is an impressive testament to the explanatory power of ⇤CDM. Earlier
versions of similar plots can be found in, for example, White et al. (1994), Scott et al. (1995), Tegmark & Zaldarriaga (2002), and
Tegmark et al. (2004). A comparison with those papers shows that the evolution of the field in the last two decades has been
dramatic, with ⇤CDM continuing to provide a good fit on these scales.
ering three orders of magnitude in scale and much of cosmic a precision test of the theory. In fact, the comparison can be done
history. The level of agreement, assuming the ⇤CDM model, to such high accuracy that it is best phrased as a scaling, AL , of
is quite remarkable. That structure grows through gravitational the theoretical prediction – taking into account the distributed ef-
instability in a dark-matter-dominated Universe seems well es- fects of lensing, etc. We find AL = 0.997±0.031, which provides
tablished, and the power of the model to explain a wide range a stunning confirmation of the gravitational instability paradigm,
of di↵erent phenomena is impressive. However, the tremendous
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3
statistical power of the Planck data, and modern probes of large- 75
and also allows us to constrain constituents of the Universe that
do not cluster on small scales (such as massive neutrinos; see
scale structure, is such that we can perform much more detailed Sect. 5.3) and so reduce the small-scale power spectrum. Future,
comparisons than this. more precise, measurements of CMB lensing will provide strong
One consistency check, which we can make internal to the constraints on neutrino masses, extra relativistic degrees of free-Cosmological Constraints and Dark Energy
n Data from these CMB missions have
already lead (and will continue to lead) to
precise measurements of many of the
important cosmological parameters
n Geometry, dark matter density, baryon
density, dark energy, the nature of
fluctuations laid down by inflation, the epoch
at which the universe was reionized and
much more
n Two critical issues that studies of the CMB
anisotropy are not well suited to address are
n What is the nature of the dark matter? Komatsu et al 2011
n What is the nature of the dark energy?
n These issues remain at the focus of ongoing
observational cosmology studies.
14. May 2021 Cosmology and Large Scale Structure - Mohr - Lecture 3 76References
n Variety of journal articles referenced in text
n “Lectures Notes on the Physics of Microwave Background
Anisotropies”, Anthony Challinor and Hieranya Peiris,
astro-ph/0903.5158
n “Lecture Notes on CMB Theory: From Nucleosynthesis to
Recombination”, Wayne Hu, astro-ph/0802.3688
n Cosmological Physics
John Peacock, Cambridge University Press, 1999
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