# Presentation: 146430

## Cosmic Microwave Background

-  Cosmological Overview/Definitions
-  Temperature
-  Polarization
-  Ramifications

- Scott Dodelson
- Academic Lecture V

## Goal: Explain the Physics and Ramifications of this Plot

- Coherent picture of formation of structure in the universe

- Quantum      Mechanical Fluctuations during Inflation

- Perturbation Growth: Pressure vs. Gravity

*t ~100,000 *years

- Matter perturbations grow into non-linear structures observed today

- Photons *freestream: *Inhomogeneities turn into anisotropies

***m**, ****r **,** ****b **,** **f***

## Review of Notation

-  Scale Factor *a(t)*
-  Conformal time/comoving horizon       *dt*/*a(t) *
-  Gravitational Potential 
* *Photon distribution 
-  Will use Fourier transforms
- **x***d**3**k ***k**ei**k********x ***/(2**)**3*
*    * k is *comoving* wavenumber
-  Wavelength k-1

## Photon Distribution

-  Distribution  depends on position **x **(or wavenumber **k**), direction **n** and time t (or η).
-  Moments        Monopole:    Dipole:         Quadrupole:  
-  You might think we care only about at our position because we can’t measure it anywhere else, but ...

## We see photons today from last scattering surface at z=1100

- D* is distance to last scattering surface

-  accounts for redshifting out of potential well

## Can rewrite  as integral over Hubble radius (aH)-1

- Perturbations *outside the horizon*

## Perturbations can be decomposed into Fourier modes

- +

- =

## Slide 9

## Combine Fourier Modes to Produce Structure in our Universe

- +

- =

- +

- =

## In this simple example, all modes have same wavelength/frequency

- More generally, at each wavelength/frequency, need to average over many modes to get spectrum

## Inflation produces perturbations

-  Quantum mechanical fluctuations in gravitational potential        (**k**)**k’****k-k’**Pk
- Inflation stretches wavelength beyond horizon: **k,t**becomes constant
-  Infinite number of independent perturbations w/ independent amplitudes

## Evolution of Fluctuations

## To see how perturbations evolve, need to solve an infinite hierarchy of coupled differential equations

- Perturbations in metric induce photon, dark matter perturbations

## Evolution upon re-entry

-  Pressure of radiation acts against clumping
-  If a region gets overdense, pressure acts to reduce the density: restoring force
-  Similar to height of guitar string (pressure replaced by tension)

## Before recombination, electrons and photons are tightly coupled: equations reduce to

- Displacement of a string

- Temperature perturbation

- Very similar to ...

## What spectrum is produced by a stringed instrument

- C string on a ukulele

## Compare the ukulele spectrum to CMB spectrum

## CMB is different because ...

-  Fourier Transform of spatial, not temporal, signal
-  Time scale much longer (400,000 yrs vs. 1/260 sec)
- No finite length: all k allowed!

## Largest Wavelength/Smallest Frequency

- Largest Wavelength/Smallest Frequency

- Smallest Wavelength/Largest Frequency

## Why peaks and troughs?

-  Vibrating String: Characteristic frequencies because ends are tied down
-  Temperature in the Universe: Small scale modes enter the horizon earlier than large scale modes

## The spectrum at last scattering is:

*Θ**0 **+ **Ψ** *~ cos[*k r**s**(**η*****) *]

- Peaks at *k = n**π**/r**s**(**η*****)*

## One more effect: Damping on small scales

- But

- So

## On scales smaller than D (or k>kD) perturbations are damped

- Fourier transformof temperature atLast Scattering Surface

- Anisotropy spectrum today

- Cl simply related to [0+]RMS(k=l/D*)

## Remember that at anywavelength, we are averaging over many modes with different direction.

- Remember that at anywavelength, we are averaging over many modes with different direction.

## Puzzle: Why are all modes in phase?

- The perturbation corresponding to each mode can either have zero initial velocity or zero initial amplitude

- We implicitly assumed that **every **mode started with zero velocity.

## Interference could destroy peak structure

- There are many, many modes with similar values of k. All have different initial amplitude. But all are in phase.

- First Peak

## An infinite number of ukuleles are synchronized 

- Similarly, all modes corresponding to first trough are in phase: they all have zero amplitude at recombination

## Without synchronization:

- First “Peak”

- First “Trough”

## All modes remain constant until they re-enter horizon.

- Inflation synchronizes all modes

- 

## How do inhomogeneities at last scattering show up as anisotropies today?

- Perturbation w/ wavelength k-1 shows up as anisotropy on angular scale ***~k**-1**/D*** **~l**-1*

## When we see this, we conclude that modes were set in phase during inflation!

- Bennett et al. 2003

*NASA/WMAP*

## Compton Scattering produces polarized radiation field

- B-mode smoking gun signature of tensor perturbations,
- dramatic proof of inflation... We will focus on E.

- Polarization field decomposes into 2-modes:

## Three Step argument for <TE>

-  E-Polarization proportional to quadrupole
-  Quadrupole proportional to dipole
-  Dipole out of phase with monopole

## Isotropic radiation field produces no polarization after Compton scattering

*Modern Cosmology*
- Adapted from Hu & White 1997

- Radiation with a dipole produces no polarization

- A quadrupole is needed

## Quadrupole proportional to dipole

- Dipole is out of phase with monopole

- Roughly,

- The product of monopole and dipole is initially positive (but small, since dipole vanishes as k goes to zero); and then switches signs several times.

## DASI initially detected TE signal

- Kovac et al. 2002

## WMAP has indisputable evidence that monopole and dipole are out of phase

- This is most remarkable for scales around l~100, which
- were not in causal contact at recombination.

- NASA/WMAP

## Different Geometries Possible

## Inflation predicts a flat universe

## We now have a solid argument that the total density is flat

- Object with known physical size

## Parameter I: Curvature

-  Same wavelength subtends smaller angle in an open universe
-  Peaks appear on smaller scales in open universe

## Hot/cold spots of known physical size has been observed

## Angular size demonstrates flatness

## Parameters II

- Reionization lowers the signal on small scales
- A tilted primordial spectrum (n<1) increasingly reduces signal on small scales
- Tensors reduce the scalar normalization, and thus the small scale signal

- n is degenerate w/ reionization, but polarization pins down the latter: we now know n to within a few percent.

## Parameters III

- Baryons accentuate odd/even peak disparity
- Less matter implies changing potentials, greater driving force, higher peak amplitudes
- Cosmological constant changes the distance to LSS

## E.g.: Baryon density

- Here, F is forcing term due to gravity.

- As baryon density goes up, frequency goes down. Greater odd/even peak disparity.

## Bottom line

*h* often used instead of

- CMB data says matter density is only 30% of critical: Need Dark Energy and Dark Matter

## Conclusions

-  Strong evidence for inflation from CMB anisotropy/polarization spectra
-  Baryon and matter densities tightly constrained,  consistent with other determinations. Dark energy & dark matter needed
-  Connection between particle physics & cosmology (inflation, dark matter, dark energy) more solid than ever. We need new tools ...

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