• Introduction
• Temperature Maps
  • Earth
  • Monopole
  • Dipole
  • COBE
  • Power
  • Precision
  • Features
• Thermal History
  • Expansion
  • Plasma
  • Glue
  • Pressure
  • Thermal
• Acoustic Oscillations
  • Gravity
  • Plane Waves
  • Harmonics
  • Extrema
• Angular Peaks
  • Spatial/Angular
  • Oscillation
  • Freeze Frame
  • Streaming
  • Soundscape
• First Peak
  • Data
  • Curvature
  • Flatness
  • Dark Energy
  • Summary
• Second Peak
  • Data
  • Inertia
  • Baryonmeter
  • Power
  • Dark Baryons
  • Summary
• Higher Peaks
  • Driving Force
  • Power
  • Summary
• Damping Tail
  • Diffusion
  • Ruler
  • Consistency
  • Summary
• Parameter Estimation
  • Parameters
  • Degeneracy
• Polarization
  • What and Why
  • Scattering
  • Projection
  • Power
  • Quadrupoles
  • B-modes
  • Gravity Waves
• Summary

Summary

Introduction

• Recent CMB experiments have revealed sound waves in the fine angular scale structure of the temperature anisotropies.
• Sound waves can be used to probe the infant universe as a kind of cosmic ultrasound
• The era of precision cosmology has begun

Temperature Maps

• Maps represent the spherical sky or Earth on a plane

• The CMB temperature on the sky is remarkably uniform

• At the level of 1 part in 1000, the CMB temperature varies because of our motion with respect to it.

• COBE showed that the CMB temperature varied at a level of 1 part in 100,000
• Variations are consistent with begin the quantum noise from inflation that formed structure through gravitational instability

• The power spectrum characterizes the size of the fluctuations as a function of angular scale
• COBE meaured only the largest angular scales in the power spectrum
• At smaller angular scales, features are expected in the power spectrum

• Current generation of experiments measure the fine scale structure of the CMB temperature maps
• Explosion of new data in recent years have ushered in the age of precision cosmology

• Features have been measured in the power spectrum

Thermal History

• Objects seem to receed as the universe expands
• Wavelength of CMB photons stretches withthe expansion
• Temperature of the CMB drops with the expansion

• Photons get hotter as one goes backwards in time.
• At 3000K, CMB photons ionize hydrogen
• Above this temperature, the universe was a photon-baryon (proton) plasma

• Thomson scattering couples photons to electrons
• Electromagnetic interactions couple electrons to baryons
• The plasma behaves as a nearly perfect fluid

• Photons provide radiation pressure
• Pressure opposes the squeezing or compression of the fluid
• Resulting oscillations are called sound waves

• Ionization/Recombination
• Tightly-coupled photon-baryon fluid
• Compression results in acoustic oscillations or sound waves

Acoustic Oscillations

• Gravity tries to compress the fluid in potential wells.
• Photon pressure resists compression resulting in acoustic oscillations
• System is equivalent to a mass on a spring falling under gravity

• Quantum fluctuations from the early universe generates both density enhancements and deficits
• Potential hills appear in regions of deficit; wells in regions of enhancement.
• Compression in the wells corresponds to rarefaction in the hills

• Pattern of sound imprinted in the temperature of CMB
• Compressed regions hotter
• Rarefied regions colder

• Potential fluctuations on all scales
• Each mode oscillates independently
• Modes that are half as long oscillate twice as fast

• Oscillations are frozen in at recombination
• Modes caught at extrema of their oscillation represent peaks ? characteristic scales with enhanced temperature fluctuations
• The wavenumbers (or spatial frequency) of the peaks are harmonically related to the fundamental scale ? the distance sound can travel by recombination

Angular Peaks

• Acoustic oscillations cause a spatial variation in the CMB temperature that oscillates in time.
• An observer right around recombination will see an essenentially isotropic CMB (same temperature in all directions)

• Standing wave acoustic oscillations
• Modes caught in extrema of their oscillations have enhanced temperature variations

• Phase of the oscillation frozen in at recombination
• Rapid change from fluid behavior to streaming behavior

• As time progresses, radiation from more distant regions reach us.
• Spatial temperature variations are viewed as angular variations of an increasingly fine angular scale

• Harmonic peaks in angular wavenumber (or multipole)

First Peak

• First peak precisely measured
• Decade long series of experimental efforts localized position
• Boomerang and Maxima experiments measured shape in 2000
• Shape and position are in beautiful agreement with predictions from standard cosmological models

• Position of peaks mainly sensitive to curvature
• Shapes fixed by the physical density of matter and baryons
• Missing or "dark energy" plays a small roll in the position of peaks

• First peak position consistent with flat universe
• Precision currently limited by uncertainties in the Hubble constant through the physical density of the dark matter
• Main ambiguity will be removed by measuring higher peaks.

• CMB indicates the total energy density is close to critical (flat universe)
• Many observations indicate that the dark matter energy density is sub-critical
• Dark energy is required to make these statements consistent
• Amount of dark energy is consistent with that needed to explain distant supernovae

• First peak shows the universe is close to spatially flat

Second Peak

• Second peak is essentially incontrovertable evidence of inflationary sound waves
• As of May 2001, the first detections
of the second peak have been reported by the DASI, Boomerang and Maxima experiments

• Baryons load down the photon-baryon oscillations
• Compression in potential wells enhanced over rarefactions

• Asymmetric oscillations due to baryons enhance compressional phase inside wells
• Amplitude of odd peaks enhanced over even peaks

• Power spectrum shows baryons enhance every other peak.
• Second peak is suppressed compared with the first and third
• Additional effects on the peak position and damping yield consistency checks

• Second peak is observed to be substantially lower than first peak
• Dark baryons of at least the big-bang nucleosynethesis density required

• First peak shows the universe is close to spatially flat
• Second peak indicate substantial amounts of dark baryons
consistent with nucleosynthesis inferences

Higher Peaks

• Radiation dominates the universe early on
• Pressure support in the radiation causes the gravitational potential to decay
• The decay occurs at exactly the right time to drive the amplitude of the oscillations up
• The higher peaks began their oscillation in the radiation dominated universe and have an enhanced amplitude.

• Raising the dark matter density reduces the overall amplitude of the peaks.
• Lowering the dark matter density eliminates the baryon loading effect so that a high third peak is an indication of dark matter.
• With three peaks, its effects are distinct from the baryons
• Measuring the dark matter density resolves the main ambiguity in the curvature measurement

• First peak shows the universe is close to spatially flat
• Constraints on the second peak indicate substantial amounts of dark baryons
• Third peak will measure the physical density of the dark matter

Damping Tail

• CMB photons bounce around (random walk through) the baryons during recombination
• For fluctuations with a short wavelength, hot and cold photons mix
• The acoustic peaks are exponentially damped on scales smaller than the distance photons random walk during recombination

• The damping scale provides another standard ruler for the curvature test
• The physical scale of the damping depends on the baryon density through the mean free path
• And the matter density through the time available for the photons to random walk.

• Raising the baryon density shifts the damping tail to higher multipoles
• Raising the matter density shifts the damping tail to lower multipoles
• Consistency checks from the damping tail will verify or falsify our assumptions about recombination and initial conditions.

• First peak shows the universe is close to spatially flat
• Constraints on the second peak indicate substantial amounts of dark baryons
• Third peak will measure the physical density of the dark matter
• Damping tail will provide consistency checks of underlying assumptions

• Precision of parameter estimation depends on instrumental noise, resolution, and sample variance

• CMB anisotropies are sensitive to a host of cosmological parameters
• Precision of parameter estimation also depends on parameter degeneracies
• External information, CMB polarization, and secondary anisotropies can break degeneracies

Polarization

• Thomson scattering polarizes light much as reflection of f of a surface
• A quadrupole temperature anisotropy generates linear polarization

• A quadrupole anisotropy is generated by the diffusion of photons
• The polarized fraction of the anisotropy is <10% since diffusion of photons only begins to take place near the end of recombination
• The coherence scale of the polarization is related to the diffusion scale
• Large-scale fluctuations in the polarization are absent

• Polarization power peaks near the diffusion scale
• Amplitude is at the 1 part per million level (micro Kelvin)
• Large scale polarization at the 1 part per 10 million level (tenth of micro Kelvin) is generated by rescattering during reionization

• Quadrupole anisotropies are associated with density, vorticity and gravitational wave fluctuations
• Their projection determines the polarization pattern and may be distinguished by symmetry properties

• Polarization patterns separate geometrically into E and B modes
• B-modes possess a handedness
• Gravitational waves generate B-modes; density fluctuations do not

• Gravitational waves show  a power spectrum with both E and B mode contributions
• Limits on the gravitational wave contribution to the temperature anisotropy imply B-modes < a few tenths of a μK.
• Gravitational waves probe the physics of inflation but will require a thorough understanding of foregrounds and secondary effects for their detection.