Observational Cosmology (C. Porciani / K. Basu) Lectures 2 + 4 The - - PowerPoint PPT Presentation

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Course website: http://www.astro.uni-bonn.de/~kbasu/ObsCosmo

Lectures 2 + 4 The Cosmic Microwave Background

Observational Cosmology

(C. Porciani / K. Basu)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Outline of the CMB Lectures

2

Lecture 1

➡ Discovery of the CMB ➡ Thermal spectrum of the CMB ➡ Temperature anisotropies

and the angular power spectrum

➡ Physical origin of the

temperature anisotropies

➡ CMB secondary anisotropies

Lecture 2

➡ Cosmological parameter

estimation

➡ Planck 2013 results - what’s

new and exiting?

➡ CMB Polarization and its

measurement - Planck & BICEP2

➡ Basics of CMB analysis: map

making and foreground subtraction

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Microwave Background Radiation

3

~ 1%

~ 400 photons per cm3 ~1 eV/cm3

• CMB dominates the radiation content of the universe
• It contains nearly 93% of the radiation energy density

and 99% of all the photons (and gives rise to the high baryon-to-photon ratio!)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Discovery of the CMB

McKellar (1940)

4

• In 1940, McKellar discovers CN molecules in interstellar space from

their absorption spectra (one of the first IS-molecules)

• From the excitation ratios, he infers the “rotational temperature of

interstellar space” to be 2° K (1941, PASP 53, 233)

• In his 1950 book, the Nobel prize winning spectroscopist Herzberg

remarks: “From the intensity ratio of the lines with K=0 and K=1 a rotational temperature of 2.3° K follows, which has of course only a very restricted meaning.”

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Discovery of the CMB

5

• After the “α-β-γ paper”, Alpher & Herman

(1948) predict 5 K radiation background as by-product of their theory of the nucleosynthesis in the early universe (with no suggestion of its detectability).

• Shmaonov (1957) measures an uniform

noise temperature of 4±3 K at λ=3.2 cm.

• Doroshkevich & Novikov (1964) emphasize

the detectability of this radiation, predict that the spectrum of the relict radiation will be a blackbody, and also mention that the twenty- foot horn reflector at the Bell Laboratories will be the best instrument for detecting it! No Nobel prize for these guys!

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Discovery of the CMB

6

• Originally

wanted to measure Galactic emission at λ=7.3 cm

• Found

a direction- independent noise (3.5±1.0

K) that they could not get rid

• f, despite drastic measures
• So

they talked with colleagues..

• Explanation of this “excess

noise” was given in a companion paper by Robert Dicke and collaborators (no Nobel prize for Dicke either, not to mention Gamow!)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

The Last Scattering Surface

7

All photons have travelled roughly the same distance since recombination. We can think of the CMB being emitted from inside of a spherical surface, we’re at the center. (This surface has a thickness)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

The last scattering “sphere”

8

anisotropy amplitude ΔT/T ~ 10−5

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Horizon scale at Last Scattering

9

This tells us that scales larger than 1.7◦ in the sky were not in causal contact at the time of last

• scattering. However, the fact that we measure the

same mean temperature across the entire sky suggests that all scales were once in causal contact

• this led to the idea of Inflation.

Inflationary theories suggests that the Universe went through a period of very fast expansion, which would have stretched a small, causally connected patch of the Universe into a region of size comparable to the size of the observable Universe today. The particle horizon length at the time of last scattering (i.e. the distance light could travel since big bang) is give by The factor 2c/H0R0 is the comoving distance to LSS.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Thickness of the last scattering “surface”

10

The visibility function is defined as the probability density that a photon is last scattered at redshift z: g(z) ~ exp(-τ) dτ/dz Probability distribution is well described by Gaussian with mean z ~ 1100 and standard deviation δz ~ 80.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 11

The temperature of last scattering depends very weakly on the cosmological parameters (weaker than logarithmically). It is mainly determined by the ionization potential of hydrogen and the photon-to-baryon ratio. Ne ~ 500 cm-3 (roughly same as Galactic HII regions!) Te = Tr = 2970 K = 0.26 eV zr = 1090 Why this is so low compared to ionization potential of hydrogen, 13.6 eV?

Recombination temperature & redshift

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Recombination temperature & redshift

12

Our goal is to calculate the temperature (and redshift) of the epoch of recombination from the above photon-to-baryon ratio and H ionization potential Q = 13.6 eV We need Saha’s ionization equilibrium equation, which in terms of ionization fraction X (since ne = np) and photon-to-baryon ratio η reads as

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Recombination temperature & redshift

13

Recombination is a gradual process. If we define the moment of recombination when X = 1/2, we get

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 14

Epoch of decoupling

The photon scattering rate is controlled by how many electrons are available: Recombination and photon decoupling takes place in matter dominated era, so from Friedmann equation: Setting Γ ~ H (condition for photon free streaming), we get Actually, when Γ ~ H, the system is not in equilibrium (Saha equation not valid)! A more precise calculation yields

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 15

The thermal spectrum

• f the CMB

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

The CMB blackbody

16

The blackbody shape is preserved at all redshifts, if expansion is purely

• adiabatic. The frequency shifts by 1/a, and energy density by 1/a4.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Measurement of TCMB

17

Ground- and balloon-based experiments have been measuring CMB temperature for decades with increasing precision but it was realized that one has to go to the stable thermal environment of outer space to get a really accurate measurement. Measured blackbody spectrum of the CMB, with fit to various data

Credit: D. Samtleben Credit: Ned Wright

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

COBE

18

Launched on Nov. 1989 on a Delta rocket. DIRBE: Measured the absolute sky brightness in the 1-240 μm wavelength range, to search for the Infrared Background FIRAS: Measured the spectrum of the CMB, finding it to be an almost perfect blackbody with T0 = 2.725 ± 0.002 K DMR: Found “anisotropies” in the CMB for the first time, at a level of 1 part in 105

2006 Nobel prize in physics

Credit: NASA

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

FIRAS on COBE

19

Far Infra-Red Absolute Spectrophotometer

A difgerential polarizing Michelson interferometer

• One input is either the sky or a

blackbody, other is a pretty good blackbody

• Zero output when the two inputs

are equal

• Internal reference kept at T0 (“cold

load”), to minimize non-linear response of the detectors

• Residual is the measurement!

Credit: NASA

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

FIRAS Measurements

20

Fundamental FIRAS measurement is the plot at the bottom: the difgerence between the CMB and the best-fitting blackbody. The top plot shows this residual added to the theoretical blackbody spectrum at the best fitting cold load temperature. The three curves in the lower panel represents three likely non-blackbody spectra: Red and blue curves show efgect

• f hot electrons adding energy

before and after recombination, the grey curve shows efgect of a non-perfect blackbody as calibrator (less than 10-4)

Credit: Ned Wright

Process that changes photon energy, not number: Compton scattering: e + γ = e + γ Processes that creates photons: Radiative (double) Compton scattering: e + γ = e + γ + γ Bremsstrahlung: e + Z = e + Z + γ

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Thermalization of the CMB

21

At an early enough epoch, timescale of thermal processes must be shorter than the expansion timescale. They are equal at z~2x106, or roughly two months after the big bang. The universe reaches thermal equilibrium by this time through scattering and photon-generating processes. Thermal equilibrium generates a blackbody radiation field. Any energy injection before this time cannot leave any spectral signature on the CMB blackbody. For pure adiabatic expansion of the universe afterwards, a blackbody spectrum —

• nce established — should be maintained.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Bose-Einstein spectrum

22

Kinetic equilibrium can be established by any process with a timescale less than H-1 Under KE, as opposed to thermal equilibrium, the spectrum is Bose-Einstein: n = [ exp(hν/kT + μ) − 1] −1 Clearly, μ plays a only small role at high frequencies, but the discrepancy becomes larger as the frequency drops. True thermal equilibrium requires the creation and destruction of photons as well as energy redistribution by scattering (see, for instance, Kompaneets, 1957). In the early Universe, both radiative Compton and bremsstrahlung processes permit the generation of photons needed to ensure true thermal equilibrium.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Bose-Einstein spectrum

23

The claim that thermal equilibrium is established at the high redshift of ~2 × 106 is equivalent to the claim that μ is driven essentially to zero by that redshift. However, if energy is added to the CMB radiation field after an epoch corresponding to a redshift of ~2×106, there may still be time to reintroduce kinetic equilibrium, but not full thermal

• equilibrium. In that case, the spectrum would be a Bose-Einstein spectrum.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 24

At a later epoch (up to recombination and during reionization) any energy input will create a y-type distortion. Here Comptonization is ineffjcient ( Γ > H−1), so we get y << 1.

μ- and y-type distortions

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

μ- and y-type distortions

25

Ref: Khatri & Sunyaev, arXiv:1203.2601

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Current limits on Spectral Distortions

26

• Energy added after z~2x106 will show up as spectral
• distortions. Departure from a Planck spectrum at fixed T is

known as “μ distortion” (B-E distribution). μ distortion is easier to detect at wavelengths λ >10 cm. COBE measurement: |μ| < 9 x 10-5 (95% CL)

• The amount of inverse Compton scattering at later epochs

(z < 105) show up as “y distortion”, where y ~ σT ne kTe (e.g. the Sunyaev-Zel’dovich efgect). This rules out a uniform intergalactic plasma as the source for X-ray background. COBE measurement: y < 1.2 x 10-5 (95% CL)

• Energy injection at much later epochs (z << 105), e.g.

free-free distortions, are also tightly constrained. COBE measurement: Yfg < 1.9 x 10-5 (95% CL)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

μ- and y-type distortions

27

Sensitivity of the proposed Pixie satellite Kogut et al. (2011), arXiv:1105.2044

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Future missions for spectral measurement

28

Cosmic Origins Explorer (PRISM, CoRE+) Pixie satellite concept

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Recombination stages

29

Sunyaev & Chluba (2009)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Spectral features during recombination

30

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 31

Temperature anisotropies

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Amplitude of temp. anisotropies

32

CMB is primarily a uniform glow across the sky! Turning up the contrast, dipole pattern becomes prominent at a level of 10-3. This is from the motion of the Sun relative to the CMB. Enhancing the contrast further (at the level of 10-5, and after subtracting the dipole, temperature anisotropies appear.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

The CMB dipole

33 I’(ν’)=(1+(v/c) cos θ)3 I(ν) ν’=(1+(v/c) cos θ) ν T(θ)=T (1+(v/c) cos θ)

• Measured velocity: 390±30 km/s
• After subtracting out the rotation and revolution of the Earth, the velocity of the

Sun in the Galaxy and the motion of the Milky Way in the Local Group one finds: v = 627 ± 22 km/s

• Towards Hydra-Centaurus, l=276±3° b=30±3°

Can we measure an intrinsic CMB dipole ?

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Doppler efgects on CMB (~β2 efgects)

34

Planck collaboration (2013)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Anisotropy amplitude

35

From the fact that non-linear structures exist today in the Universe, the linear growth theory predicts that density perturbations at z = 1100 (the time of CMB release) must have been of the order of After the CMB was found in 1965, fluctuations were sought at the relative level

• f 10-3, but they were not found. Eventually they were found at a level of 10-5.

The reason is that already before the CMB release the DM perturbations started growing independently. While the radiation-Baryon fluid oscillated and therefore didn’t grow in amplitude, the DM perturbations continued to grow. Before the DM dominated the mass (i.e. z~3300) this growth was slow (logarithmic), while

• nce DM dominate the mass the growth was linear. Since DM has no coupling to

the electromagnetic spectrum, nor to the baryons, this growth happened without pumping the perturbations in the CMB to equal levels. In fact, this can be seen as a proof of the existence of such a DM as a non- interacting form of matter!

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

DMR on COBE

36

Difgerential Microwave Radiometer

• Difgerential radiometers measured at

frequencies 31.5, 53 and 90 GHz, over a 4-year period

• Comparative measurements of the

sky ofger far greater sensitivity than absolute measurements

Credit: NASA

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

COBE DMR Measurements

37 Credit: NASA Credit: Archeops team

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

WMAP: 2001-2010

38

Note the same dual receivers as COBE. This design, plus the very stable conditions at the L2, minimizes the “1/ f noise” in amplifiers and receivers. Thus after 7 years, the data could still be added and noise lowered (of course, the improvement will be marginal).

Credit: NASA

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

WMAP results after 1st year

39

Internal Linear Combination map

(Credit: WMAP Science Team)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Planck results after 1.5 years

40

(next lecture)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

CMB temperature anisotropies

41

• The basic observable is the CMB intensity as a function of frequency

and direction on the sky. Since the CMB spectrum is an extremely good black body with a fairly constant temperature across the sky, we generally describe this observable in terms of a temperature fluctuation

• The equivalent of the Fourier expansion on a sphere is achieved by

expanding the temperature fluctuations in spherical harmonics

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Analogy: Fourier series

42

Sum sine waves of difgerent frequencies to approximate any function. Each has a coeffjcient, or amplitude.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Spherical harmonics

43

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 44

Spherical harmonics

l~180º/θ relates to the angular size of the pattern, whereas m relates to

the orientation of the pattern. Thus〈|alm|2〉is independent of m.

The mean〈alm〉is zero, but we want to calculate its variance:

(Reason is the S-W efgect!)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 45

Visualizing the multipoles

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Visualizing the multipoles (real sky!)

46

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Power at difgerent scales

47 Credit: Wayne Hu

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

CMB power spectrum

48

Use spherical harmonics in place of sine waves: Calculate coeffjcients, alm, and then the statistical average: Amplitude of fluctuations on each scale ⎯ that’s what we plot. (TT power spectrum)

How to constrain cosmology from this measurement?

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Make your own CMB experiment!

49

• Design experiment to measure
• Find component amplitudes
• Plot against l (where l is inverse of angular scale, l ~ π / θ )

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Generating theoretical Cl

50

OUTPUT INPUT Fit to data

Favorite cosmological model: Ωm, ΩΛ, σ8, H0, ..

Physics

powerful cosmological codes (CMBFast or CAMB)

??

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 51

We only have one Universe, so we are intrinsically limited to the number of independent m-modes we can measure − there are only (2l + 1) of these for each multipole. We obtained the following expression for the power spectrum: For an idealized full-sky observation, the variance of each measured Cl is: How well we can estimate an average value from a sample depends on how many points we have on the sample. This is called the cosmic variance, and it is an unavoidable source of uncertainty when constraining models!

Cosmic variance

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Cosmic and sample variance

52

• Cosmic variance: on scale l,

there are only 2l+1 independent modes

• Averaging over l in bands of Δl ≈1

makes the error scale as l-1

• If the fraction of sky covered is f,

then the errors are increased by a factor 1/√fsky and the resulting variance is called

sample variance (f ~0.65 for the PLANCK

satellite)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

The origin of temperature anisotropies

53

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Primordial temperature anisotropies

54

At recombination, when the CMB was released, structure had started to form This created the “hot” and “cold” spots in the CMB These were the seeds of structure we see today

Please don’t confuse between the “creation”

• f the CMB photons, and their “release” from

the last scattering surface! CMB photons are created at much earlier e p o c h t h r o u g h m a t t e r / a n t i - m a t t e r annihilation, and thus, were formed as g a m m a r a y s ( n o w c o o l e d d o w n t o microwave)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Creation of anisotropies

55

Primordial temperature anisotropies

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Sources of ΔT

56

Max Tegmark (astro-ph/9511148)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Power spectrum: primary anisotropies

57

Acoustic peaks Damping tail Sachs-Wolfe plateau

• Perturbations in the gravitational potential (Sachs-Wolfe efgect):

photons that last scattered within high-density regions have to climb out

• f potential wells and are thus redshifted
• Intrinsic adiabatic perturbations (the acoustic peaks): in high-density

regions, the coupling of matter and radiation will also compress the radiation, giving a higher temperature

• Velocity perturbations (the Doppler troughs): photons last-scattered

by matter with a non-zero velocity along the line-of-sight will receive a Doppler shift

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Sources of primary anisotropies

58

Quantum density fluctuations in the dark matter were amplified by inflation. Gravitational potential wells (or “hills”) developed, baryons fell in (or moved away). Various related physical processes afgected the CMB photons:

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Sachs-Wolfe efgect

59

Δν/ν ~ Δ T/T ~ Φ/c2

As we explain below, additional efgect of time dilation while the potential evolves leads to a factor of 1/3 (e.g. White & Hu 1997):

The temperature fluctuations due to the so-called Sachs-Wolfe efgect are due to two competing efgects: (1) the redshift experienced by the photon as it climbs out of the potential well toward us and (2) the delay in the release of the radiation, leading to less cosmological redshift compared to the average CMB radiation.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 60

The second contribution (redshift due to time delay) is more tricky. Because of general relativity, the proper time goes slower inside the potential well than outside. The cooling of the gas in this potential well thus also goes slower, and it therefore reaches 3000 K at a later time relative to the average Universe.

Sachs-Wolfe efgect

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 61

Sachs-Wolfe efgect

For power-law index of unity for the primary density perturbations, ns=1 (Zel’dovich, Harrison ~1970), the Sachs-Wolfe efgect produces a flat power spectrum: Cl SW ~ 1/ l (l+1).

(For Sachs-Wolfe efgect)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Measuring Cl at low multipoles (l≤100)

62

The horizon scale at the surface of last scattering (z ~ 1100) corresponds roughly to 2°. At scales larger than this (l ≥ 100), we thus see the power spectrum imprinted during the inflationary epoch, unafgected by later, causal, physical processes. Due to the limit of cosmic variance, the measurements by COBE some ~25 years ago was already of adequate accuracy!

• Baryons fall into dark matter potential wells: Photon baryon fluid heats up
• Radiation pressure from photons resists collapse, overcomes gravity,

expands: Photon-baryon fluid cools down

• Oscillating cycles exist on all scales. Sound waves stop oscillating at

recombination when photons and baryons decouple.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Acoustic oscillations

63

Springs: photon pressure Balls: baryon mass

Credit: Wayne Hu

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Acoustic oscillations

64

Equations of motion for self-gravitating non-relativistic gas:

Continuity eqn. Euler eqn. Poisson eqn. From these three we get the perturbation equation

For radiation-dominated era, set p=ρc2/3

We want to solve for this δ.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Acoustic oscillations

65

(perturbation equation)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 66

Acoustic oscillations

The last equation is a standing wave with an interesting property: its phase is fixed by the factor in parenthesis. This means that for every wave number k we know what the phase of the

• scillating standing wave is at the time of the CMB release. For some modes this phase may be

π/2, in which case the density fluctuation has disappeared by the time of CMB release, but the motion is maximum. For others the density fluctuation may be near maximum (phase 0 or π). This gives a distinct wavy pattern in the power spectrum of the CMB.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Angular variations

67

These frames show

• ne

superhorizon temperature mode just after decoupling, with representative photons last scattering and heading toward the observer at the center. (From left to right) Just after decoupling; the

• bserver’s particle horizon when only the

temperature monopole can be detected; some time later when the quadrupole is detected; later still when the 12-pole is detected; and today, a very high, well-aligned multipole from just this single mode in k space is detected.

Animation by Wayne Hu

Density fluctuation on the sky from a single k mode, and how it appears to an observer at difgerent times:

Oscillations took place on all scales. We see temperature features from modes which had reached the extrema

• Maximally compressed regions were hotter than the average

Recombination happened later, corresponding photons experience less red-shifting by Hubble expansion: HOT SPOT

• Maximally rarified regions were cooler than the average

Recombination happened earlier, corresponding photons experience more red-shifting by Hubble expansion: COLD SPOT

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Acoustic peaks

68

1st peak harmonics

Harmonic sequence, like waves in pipes or strings: 2nd harmonic: mode compresses and rarifies by recombination 3rd harmonic: mode compresses, rarifies, compresses

➡ 2nd, 3rd, .. peaks

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Harmonic sequence

69

Modes with half the wavelengths

• sccilate twice as

fast (ν = c/λ). Peaks are equally spaced in

1 2 3

Credit: Wayne Hu

Times in between maximum compression/rarefaction, modes reached maximum velocity This produced temperature enhancements via the Doppler efgect (non-zero velocity along the line of sight) This contributes power in between the peaks

➡ Power spectrum does not go to zero (it does at very high l-s)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Doppler shifts

70

• Photon difgusion (Silk damping) suppresses fluctuations in the baryon-

photon plasma

• Recombination does not happen instantaneously and photons execute a

random walk during it. Perturbations with wavelengths which are shorter than the photon mean free path are damped (the hot and cold parts mix up)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Damping and difgusion

71

Power falls off

Thickness

• f the LSS is

comparable to the

• scillation

scales This is same as a low-resolution instrument blurs all the details!

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Power spectrum summary

72

Acoustic peaks Damping tail Sachs-Wolfe plateau ISW rise

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Which way the peaks move?

73 Credit: Wayne Hu

The presence of more baryons add inertia, and increases the amplitude

• f

the

• scillations

(baryons drag the fluid into potential wells). Perturbations are then compressed more before radiation pressure can revert the motion. This causes a breaking

• f

symmetry in the oscillations, enhancing only the compressional phase (i.e. every odd-numbered peak). This can be used to measure the abundance of cosmic baryons.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Baryon loading

74 Credit: Wayne Hu

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Baryons in the power spectrum

75

Power spectrum shows baryon enhance every other peak, which helps to distinguish baryons from cold dark matter

Credit: Wayne Hu

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

DM in the power spectrum

76

Cold dark matter Baryons

Credit: Max Tegmark

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Efgect of curvature

77

Ωk does not change the amplitude of the power spectrum, rather it shifts the peaks sideways. This follows from the conversion of the physical scales (on the LSS) to angular scales (that we observe), which depends on the geometry.

Curvature (cosmological constant, ΩΛ) also causes ISW efgect on large scales, by altering the growth of structures in the path of CMB photons.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

CMB parameter cheat sheet

78

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

SECONDARY temperature anisotropies

79

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Integrated Sachs-Wolfe efgect

80

Temperature anisotropies due to density change and associated gravitational potential (scaler perturbations) at a given point x along the direction n

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Integrated Sachs-Wolfe efgect

81

• The early ISW efgect is caused by the small but non-negligible

contribution of photons to the density of the universe

• The late ISW efgect:
• Gravitational blueshift on infall does not cancel redshift on climb-out
• Contraction of spatial metric doubles the efgect: ΔT/T ~ 2ΔΦ
• Efgect of potential hills and wells cancel out on small scales

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 82

Integrated Sachs-Wolfe efgect

ISW efgect

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

ISW efgect as Dark Energy probe

83

The ISW efgect constraints the dynamics of acceleration, be it from dark energy, non-flat geometry, or non-linear growth. Cosmic evolution of dark energy is parametrized by w(a) ≡ pDE/ρDE For a cosmological constant, w=-1. In general, ρDE ~ a -3(1+w) In the absence of curvature, measurement of ISW is measurement of DE.

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Cosmic variance problem

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Cosmic variance problem

85

Corasaniti, Giannantonio, Melchiorri 2005

Problem: Low multipole signals are severely cosmic variance limited Solution: Cross-correlate with other probes

• f dark energy, with large sky coverage

(optical, X-ray or radio surveys of galaxies)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 86

ISW optical-survey correlation

Re-scattering of CMB photons damps anisotropy power (ΔT2) as e-2τ, with τ the

• ptical depth to Thomson scattering.

For τ = 0.095, this means a 20% reduction from initial power. New perturbations are generated on small scales due to the bulk motion of electrons in over-dense regions (Ostriker-Vishniac efgect)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

ΔT from reionization

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

kSZ efgect from reionization

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kSZ anisotropy at ell ≈ 1000 - 10000 receives a substantial contribution from kSZ anisotropy due to patchy reionization (“patchy kSZ”), which arises again from ne∗vpec but, during this epoch, the fluctuations in ne are fractionally large due to the inhomogeneous nature of reionization. The amplitude of the power spectrum of patchy kSZ scales with the duration of the epoch of reionization (EoR), but there is much more information about the bubble size and velocity field during reionization to be obtained if the power spectrum’s shape (and possibly the higher moments of the field) can be measured.

CCAT White Paper

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Other small efgects..

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Resonant scattering by atoms and molecules (CMB spectroscopy!) OI 63 µm line

Basu, Hernandez-Monteagudo & Sunyaev 2004

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Power at small angular scales

90

The signal is actually Cl ! Our power spectrum plots boosts the

apparent variance at large l by a factor l2 ! Observations at high-l therefore requires far greater sensitivity.

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Local y-distortion: thermal SZ efgect

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

tSZ power spectrum

92 IR galaxies foreground

Simulation and observation

• f high-resolution CMB sky

Ramos-Ceja, Basu et al. 2014

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tSZ power and foregrounds

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SZ power spectrum is a powerful probe of cosmology, primarily through its strong dependance on σ8

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

SZ power spectrum

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SPT constraints assuming difgerent tSZ templates

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Lensing of the power spectrum

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Lensing of the power spectrum

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Lensing smooths the power spectrum (and E mode polarization) with a width ∆l~60 This is a small efgect, reaching ~10% deep in the damping tail.

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High-ell CMB bandpower measurement

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Keisler et al. 2011

Lensed CMB

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 98

CMB polarization

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How to go further with CMB?

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Cosmic Variance › We only have one realization (our sky), i.e., one event. › TT at small l (incl. first peak) is now cosmic variance limited. To go further: › TT at large l › Polarization

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Polarization of the CMB

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Measurement of polarization

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Polarization measurement is PLANCK’s holy grail TE power EE power WMAP PLANCK Measurement of the BB power spectrum!

Credit: Planck bluebook

P r e d i c t i

• n

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Detecting polarization is diffjcult!

102 Power spectra of CMB temperature anisotropies (black), grad polarization (red), and curl polarization due to the GWB (blue) and due to the lensing of the grad mode (green), all assuming a standard CDM model with T/S = 0.28. The dashed curve indicates the efgects of reionization on the grad mode for τ = 0.1.

×100 smaller ×10 smaller

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Quadrupole + Thomson scattering

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Polarization is induced by Thomson scattering, either at decoupling

• r

during a later epoch of reionization. (No circular polarization, i.e. V=0)

Two things: “Normal” CDM: Density perturbations at z=1100 lead to velocities that create local quadrupoles seen by scattering electrons. => E-mode polarization (“grad”) Gravity waves: create local quadrupoles seen by the scattering electrons. => B-mode polarization (“curl”)

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What causes the CMB quadrupole?

104

The problem of understanding the polarization pattern of the CMB thus reduces to understanding the quadrupole temperature fluctuations at the epoch of last scattering.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

From gravity wave to polarization

105

• We can break down the polarization

field into two components which we call E and B modes. This is the spin-2 analog of the gradient/curl decomposition of a vector field.

• E modes are generated by density

(scalar) perturbations via Thomson scattering.

• Additional vector modes are created

by vortical motion of the matter at recombination - this is small

• B modes are generated by gravity

waves (tensor perturbations) at last scattering or by gravitational lensing (which transforms E modes into B modes along the line of sight to us) later on.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

E and B modes

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E-mode

(“gradient-like”)

B-mode

(“curl-like”)

Two flavors of CMB polarization: Density perturbations: curl-free, “E-mode” Gravity waves: curl, “B-mode”

The Helmholtz's Theorem on Vector Fields Helmholtz's theorem is also called as the fundamental theorem of vector

• calculus. It is stated as

“A suffjciently smooth, rapidly decreasing vector field in three dimensions can be decomposed into the sum of a solenoidal (divergence-less) vector field and an irrotational (curl-less) vector field.” The theorem is also called as Helmholtz decomposition, it breaks a vector field into two orthogonal components.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 107

E and B modes: 2D vector analogy

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Polarization from the last scattering

108

We saw that polarization pattern created at the last scattering can only come from a quadrupole temperature anisotropy present at that epoch. In terms of multipole decomposition of a radiation field in terms of spherical harmonics, Ylm (θ,φ), the five quadrupole moments are represented by

l = 2; m = 0, ±1, ±2. The orthogonality of the spherical harmonics guarantees that no other moment can generate polarization from Thomson scattering! The problem of understanding the polarization pattern of the CMB thus reduces to understanding the quadrupolar temperature fluctuations at the epoch of last scattering.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Visualization of the polarization pattern

109

The scaler quadrupole moment, l=2, m=0. Note the azimuthal symmetry in the transformation of this quadrupole anisotropy into linear polarization.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Polarization patterns

110

In general there are three sources to the quadrupole T anisotropy at recombination:

• scalers (m=0) for density fluctuations
• vectors (m=1) for vorticity (negligible)
• tensors (m=2) for gravity waves

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments 111

Polarization patterns

Scaler mode (l=2, m=0) Vector mode (l=2, m=±1) Tensor mode (l=2, m=±2) Animations by Wayne Hu

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Parity of E & B modes

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Scaler-to-Tensor ratio

113

Scaler power spectrum

The scaler perturbations are Gaussian, so all information about them is contained in the two-point correlation function: The mean square value of the initial perturbation amplitude is Where is also called the power spectrum, and is approximated as follows: In 1960’s, Zel’dovich and Harrison independently predicted the flat spectrum of perturbations (i.e. ns = 1). The WMAP5 values for a fixed k∗ = 500 Mpc-1 are:

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Scaler-to-Tensor ratio

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Inflation and tensor power spectrum

Inflation occurs if the universe is filled with a scalar field φ, which has non-vanishing scalar potential V(φ). The homogeneous field φ then satisfies the equation If H is large (the universe expands rapidly) and dV/dφ small, the field φ varies slowly in time. The Friedmann equation in this case is H2 = 8π/3 G V(φ), so if φ varies slowly, then V(φ) and thus H also varies slowly, and the parameters of inflation are almost time independent. Yet, the parameters are not exactly time-independent at inflation, so the predicted value of the spectral tile (ns - 1) is small but non-zero. It can ve positive or negative, depending on the scalar potential V(φ). In particular, it is negative for the simplest power-law potentials like

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Scaler-to-Tensor ratio

115

Inflation and tensor power spectrum

Actually, the derivation of approximately flat power spectrum does not depend on whether we deal with scalar or tensor fields. So inflation also generates tensor perturbations (transverse traceless perturbations of spatial metric hij, i.e. gravitational waves). We have the same picture for tensor perturbations: primordial perturbations are Gaussian random field with almost flat power spectrum. In this case we have It is convenient to introduce the parameter which measures the ratio of tensor to scalar perturbations. For simple inflation theories with power-law potentials (last slide), prediction is r ~ 0.1 − 0.3.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Polarization power spectra

116

TT Tensors TE EE Lensing BB for r=0.5 BB for r=10-4

E & B modes have difgerent reflection properties (“parities”): Parity: (-1)l for E and (-1)l+1 for B

The cross-correlation between B and E or B and T vanishes (unless there are parity- violating interactions), because B has opposite parity to T or E. We are therefore left with 4 fundamental observables. r = T/S: Tensor to scaler ratio, generated by the primordial gravity waves at last scattering

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Polarization power spectra

117

The polarization power also exhibits acoustic

• scillations since the

quadrupole anisotropies that generate it are themselves formed from the acoustic motion of the fluid. The EE peaks are out of phase with TT peaks since scaler perturbation efgect is maximum when the velocity field is maximum.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Shape of the power spectra

118

reionization bump

• The primordial B-mode signal

(due to a stochastic background of gravitational waves) dominates

• nly

at intermediate angular scales

• On very large scales, the

polarization signal is dominated by secondary fluctuations imprinted by reionization

• The

lens-generated signal grows at smaller scales

Shape and amplitude of EE are predicted by ΛCDM. Shape of BB is predicted “scale-invariant gravity waves”. Amplitude of BB is model dependent, and not really constrained from theory. Measuring this amplitude would provide a direct handle of the energy scale of inflation!

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

EE power spectrum

119

MCMC simulations from K. Vanderlinde

The intermediate to small scale polarization signal is sensitive only to the physics at the epoch of last scattering (unlike TT which can be modified). The EE spectrum is already well constrained from the cosmological models, but it provides additional checks and helps to break some degeneracies.

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

BB spectrum uncertainties

120

MCMC simulations from K. Vanderlinde

Tensors Lensing

BB mode can tell us about a lot of new physics (energy scale at inflation, neutrino mass, etc.), but its prediction is still very uncertain.

Before March 2014, data only put a limit: r = T/S < 0.3

• The DASI experiment at the South Pole

was the first to detect E-mode CMB polarization

• It was followed by WMAP’s measurement
• f CTE(l) for l<500
• Both the BOOMERANG and the CBI

experiments have reported measurements of CTT, CTE , CEE and a non-detection of B modes

• E-mode has also been measured by

CAPMAP and Maxipol

• B-mode polarization has not been

detected yet (current noise level is 50 K at the arcmin scale, future ground- based experiment will go down to 5 K)

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Detection of E-mode polarization

121

DASI collaboration, 2002

Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

BICEP2 E- and B-mode CMB maps

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Observational Cosmology Lectures 2+4 (K. Basu): CMB theory and experiments

Questions?

123