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  • CMB Introduction
    448 University of Chicago Astronomy Department KICP Thunch astro ph CO ADS InSpire 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 Polarization Power Spectrum Key Concepts 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 The power spectrum of the polarization associated with the initial density perturbations shows several characteristics It peaks near the diffusion scale l 1000 at a level that represents 10 polarization of the anisotropies and hence a several micro Kelvin signal It has a second peak on large angular scales representing the same Thomson scattering process but arising from recent times when the hydrogen in

    Original URL path: http://background.uchicago.edu/~whu/intermediate/Polarization/polar3.html (2015-06-26)
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  • CMB Introduction
    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 Quadrupole Types and Polarization Patterns Key Concepts Quadrupole anisotropies are associated with density vorticity and gravitational wave fluctuations Their projection determines the polarization pattern and may be distinguished by symmetry properties The polarization probe more than just the density or temperature fluctuations at recombination Because the polarization pattern is a projection of the quadrupole anisotropy any source of quadrupole anisotropy leaves its imprint in the polarization In general there are three sources to the quadrupole anisotropy at recombination Lobes the directions of the hot and cold photons Notice that the hot and cold lobes are separated by 90 degrees due to their quadrupole nature Planes represent the flucutation in intensity of the underlying plane wave fluctuation The first is the acoustic density perturbations described above Here the movement of the photons from hot to cold regions produces a symmetric quadrupole moment symmetric to rotations about the plane wave axis Vorticity in the plasma will create a different type of quadrupole due to the Doppler shift associated with the velocity fortunately vorticity perturbations are predicted to be negligible by recombination A passing gravitational wave causes an anisotropic stretching of space and correspondingly the frequency of CMB photons This also produces a quadrupolar variation in the temperature Importantly it is not symmetric like the density quadrupole This asymmetry causes a handedness to the pattern of polarization Let us consider in a little more detail how the quadrupole moment determines the polarization pattern Take the case of density fluctuations Recall that the observed polarization is aligned with the cold red lobe of the quadrupole As we observe different angles with respect to

    Original URL path: http://background.uchicago.edu/~whu/intermediate/Polarization/polar4.html (2015-06-26)
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  • CMB Introduction
    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 B modes Key Concepts Polarization patterns separate geometrically into E and B modes B modes possess a handedness Gravitational waves generate B modes density fluctuations do not In general the polarization pattern has two geometrical components Instead of describing it by the descriptions North South and East West or more formally the Stokes parameters which depend on an arbitrary choice of coordinates we can describe it by its orientation relative to itself There are two directions picked out by a polarization pattern that which is picked out by its orientation and that which is picked out by its amplitude The amplitudes of the polarization patterns described on the last page are modulated in space by the plane wave they are sitting on Here the plane wave is going in the up

    Original URL path: http://background.uchicago.edu/~whu/intermediate/Polarization/polar5.html (2015-06-26)
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  • CMB Introduction
    InSpire 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 Gravitational Waves Key Concepts 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 microKelvin Gravitational waves probe the physics of inflation but will require a thorough understanding of foregrounds and secondary effects for their detection If there were only gravitational waves and no density perturbations in the Universe the CMB temperature polarization and temperature polarization cross power spectra would look like Notice that the polarization contains power in both the E and B modes That we do see acoustic peaks in the spectrum indicates that this scenario cannot actually be true At most gravitational waves contribute a fraction

    Original URL path: http://background.uchicago.edu/~whu/intermediate/Polarization/polar6.html (2015-06-26)
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  • CMB Introduction
    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 i n 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

    Original URL path: http://background.uchicago.edu/~whu/intermediate/summary.html (2015-06-26)
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  • Cosmic Symphony
    to form the large scale structures we see today Yet what was the prime mover the source of the initial disturbances that triggered the sound waves The question is troubling Imagine yourself as an observer witnessing the big bang and the subsequent expansion At any given point you will see only a finite region of the universe that encompasses the distance light has traveled since the big bang Cosmologists call the edge of this region the horizon the place beyond which you cannot see This region continuously grows until it reaches the radius of the observable universe today Because information cannot be conveyed faster than light the horizon defines the sphere of influence of any physical mechanism As we go backward in time to search for the origin of structures of a particular physical size the horizon eventually becomes smaller than the structure Therefore no physical process that obeys causality can explain the structure s origin In cosmology this dilemma is known as the horizon problem Timeline of the Universe As inflation expanded the universe the plasma of photons and charged particles grew far beyond the horizon the edge of the region that a hypothetical viewer after inflation would see as the universe expands During the recombination period about 380 000 years later the first atoms formed and the cosmic microwave background CMB radiation was emitted After another 300 million years radiation from the first stars reionized most of the hydrogen and helium Bryan Christie Design Fortunately the theory of inflation solves the horizon problem and also provides a physical mechanism for triggering the primordial sound waves and the seeds of all structure in the universe The theory posits a new form of energy carried by a field dubbed the inflation which caused an accelerated expansion of the universe in the very first moments after the big bang As a result the observable universe we see today is only a small fraction of the observable universe before inflation Furthermore quantum fluctuations in the inflaton field magnified by the rapid expansion provide initial disturbances that are approximately equal on all scales that is the disturbances to small regions have the same magnitude as those affecting large regions These disturbances become fluctuations in the energy density from place to place in the primordial plasma Evidence supporting the theory of inflation has now been found in the detailed pattern of sound waves in the CMB Because inflation produced the density disturbances all at once in essentially the first moment of creation the phases of all the sound waves were synchronized The result was a sound spectrum with overtones much like a musical instrument s Consider blowing into a pipe that is open at both ends The fundamental frequency of the sound corresponds to a wave also called a mode of vibration with maximum air displacement at either end and minimum displacement in the middle Sonic Harmonics The sound spectrum of the early universe had overtones much like a musical instrument s If you

    Original URL path: http://background.uchicago.edu/~whu/SciAm/sym2.html (2015-06-26)
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  • Cosmic Symphony
    Spectrum The variations are barely noticeable at large scales corresponding to regions that stretch about 30 degrees across the sky c and at small scales corresponding to regions about a tenth of a degree across e But the temperature differences are quite distinct for regions about one degree across d This first peak in the power spectrum graph at bottom reveals the compressions and rarefactions caused by the fundamental wave of the early universe the subsequent peaks show the effects of the overtones Sound waves also oscillated in the plasma of the early universe After inflation the fundamental wave compressed some regions of plasma and rarefied others causing the temperature of the CMB radiation in the regions to reach maximum blue and minimum red values by the time of recombination The overtones oscillated two three or more times as quickly causing smaller regions to reach maximum and minimum CMB temperatures at the time of recombination The results show that the regions with the greatest variations subtend about one degree across the sky or nearly twice the size of the full moon At the time of recombination these regions had diameters of about one million light years but because of the 1 000 fold expansion of the universe since then each region now stretches nearly one billion light years across This first and highest peak in the power spectrum is evidence of the fundamental wave which compressed and rarefied the regions of plasma to the maximum extent at the time of recombination The subsequent peaks in the power spectrum represent the temperature variations caused by the overtones The series of peaks strongly supports the theory that inflation triggered all the sound waves at the same time If the perturbations had been continuously generated over time the power spectrum would not be

    Original URL path: http://background.uchicago.edu/~whu/SciAm/sym3.html (2015-06-26)
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  • Cosmic Symphony
    laws of Euclidean geometry and must be very close to spatially flat And because the geometry of the universe depends on its energy density this finding implies that the average energy density is close to the so called critical density about 10 29 gram per cubic centimeter The next thing cosmologists would like to know is the exact breakdown of the universe matter and energy The amplitudes of the overtones provide the key Whereas ordinary sound waves are driven solely by gas pressure the sound waves in the early universe were modified by the force of gravity Gravity compresses the gas in denser regions and depending on the phase of the sound wave can alternately enhance or counteract sonic compression and rarefaction Analyzing the modulation of the waves reveals the strength of gravity which in turn indicates the matter energy composition of the medium As in today s universe matter in the early universe fell into two main categories baryons protons and neutrons which make up the bulk of so called ordinary matter and cold dark matter which exerts gravity but has never been directly observed because it does not interact with ordinary matter or light in any noticeable way Both ordinary matter and dark matter supply mass to the primordial gas and enhance the gravitational pull but only ordinary matter undergoes the sonic compressions and rarefactions At recombination the fundamental wave is frozen in a phase where gravity enhances its compression of the denser regions of gas Gravity and sonic motion work together Influence of dark matter modulates the acoustic signals in the CMB After inflation denser regions of dark matter that have the same scale as the fundamental wave represented as troughs in this potential energy diagram pull in baryons and photons by gravitational attraction The troughs are shown in ed because gravity also reduces the temperature of any escaping photons By the time of recombination about 380 000 years later gravity and sonic motion have worked together to raise the radiation temperature in the troughs blue and lower the temperature at the peaks red But the first overtone which has half the fundamental wavelength is caught in the opposite phase gravity is attempting to compress the plasma while gas pressure is trying to expand it As a result the temperature variations caused by this overtone will be less pronounced than those caused by the fundamental wave Gravity counteracts sonic motion At smaller scales gravity and acoustic pressure sometimes end up at odds Dark matter clumps corresponding to a second peak wave maximize radiation temperature in the troughs long before recombination After this midpoint gas pressure pushes baryons and photons out of the troughs blue arrows while gravity tries to pull them back in white arrows This tug of war decreases the temperature differences which explains why the second peak in the power spectrum is lower than the first This effect explains why the second peak in the power spectrum is lower than the first And by comparing

    Original URL path: http://background.uchicago.edu/~whu/SciAm/sym3b.html (2015-06-26)
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