Naomi Pequette

Background Information

History  Predicted -- George Gamow (1948) and Ralph Alpher and Robert Herman (1950)  Detected-- Arno Penizas and Robert Wilson (1965) Dave Wilkinson and Robert Dicke - Released papers on observation and cosmological significance  Penzias and Wilson received Nobel Prize in 1978

Cosmic Microwave Background Radiation (CMBR)  Peaks in microwave part of spectrum at 2.75K  Was formed 380,000 years after Big Bang  Protons and electrons combine to form neutral hydrogen  Photons interact very weakly with the matter of early universe

 The early universe is like the clouds in the Earth’s atmosphere.  You can’t see the tops of the clouds, only the bottoms.  Maps of the CMB temperatures are of the surface of the scattering

WMAP  Launched in 2001 as replacement for COBE

OpticsDual Gregorian; 1.4 m x 1.6 m primaries ThermalPassively cooled with radiators, solar array shades instrument; MLI and gamma-alumina cylinder isolates spacecraft from instrument RedundancyPrimary Single String StructureComposite / aluminum Lifetime27 months; fuel limit > 3 years Frequencies Wavelengths (mm) Number of Channels Resolution (FWHM, degrees) <0.23

Fundamental Sound Wave Mapping this—Angular Power Spectrum Causes of the Anisotropies

The Fundamental Sound Wave  Random fluctuations (Gaussian) due propagated throughout early universe  Waves oscillating in time instead of space  Fixed by distance sound could travel before recombination

Fundamental Sound Wave  As sound wave propagates region of max. positive displacement would go toward av. temp (min. displacement) to min. temperature (max. neg. displacement)  Fundamental Tone  Harmonics (overtones) oscillate quicker, and cause smaller regions to reach max. displacement  Can be understood by breaking up into harmonics or modes

From “Four Keys to Cosmology” in Scientific American

Fourier Decomposition  Basic wave can be decomposed into fundamental harmonics  CMB Anisotropies can be expanded into terms of multipoles

Multipoles  Each mode is like a particular instrument and the whole sky map is the sound of the cosmic symphony  Each multipole labeled by number ( l = 1,2,3…)  The higher the l, the smaller the features the multipole describes  The amplitude of each mode is like the volume of each instrument

Monopole ( l = 0)  Lowest note in the cosmic note  Entire sphere pulses as one  At average temperature of CMBR  Fundamental tone

Dipole ( l = 1)  Next lowest note  Temperature goes up in one hemisphere and down in the other  Dominated by Doppler shift of solar system’s motion relative to CMBR  Sky appears hotter in direction sun is traveling

Other Multipoles Quadropole subtends about 90 degrees Octopole subtends about 60 degrees

WMAP’s View of the CMBR

Angular Power Spectrum  Plot the magnitude of temperature variations against sizes of hot and cold spots  Greatest variations ~1 degree  First and highest peak = fundamental wave  Second = 1 st harmonic

What Does this Tell Us? Angular Power Spectrum

What Does This Tell Us?  Shape of the Universe  Composition of the Universe  Effects of Dark Energy and Dark Matter  Cosmic Neutrino Abundance

Geometry of the Universe  Information from the fundamental frequency and strengths of overtones  CMBR gives us angular size of most intense temperature variation  This tells us frequency of fundamental sound wave  Given this and speed of sound, can determine size of wave  This information + knowing distance CMBR photons traveled to earth—know information about triangle formed by wave

Note!  The distance to the CMBR depends on the peaks of the angular power spectrum  This distance depends on the curvature of space-time and the history of dark energy (expansion of the universe)  This cosmic radius is not infinite, but is certainly larger than the radius of the currently visible universe

Geometry continued  Knowing the triangle—can see if angles add up to 180 degrees  Test of spatial curvature  Indeed—angles add up to 180 degrees  We live in a flat universe!!!  The fact that it is a flat universe implies average energy density is close to critical density ( g/cm 3 )  Geometry depends on energy density

Geometry continued  Another way to determine this using WMAP is the size of the features in the CMBR  The largest variations are ~1º  Flat Universe  Now know this with 2% accuracy

Composition of the Universe  Information from the amplitude of the second peak in power spectrum  Sound waves in early universe modified by gravity  Both ordinary and dark matter provide mass and enhance gravitational pull  BUT only baryonic matter undergoes sonic compressions and rarefactions.

Composition of the Unviverse  First overtone—gravity attempting to compress plasma while gas pressure trying to expand it  Thus why temp. variations are less pronounced and second peak is lower  By compare heights of two peaks  Baryons had same energy density as photons— thus constitute about 4.6% of critical density today

Dark Matter  Abundance of cold dark matter is needed for gravitational potential wells to be sufficiently deep  By measuring ratios of heights of first 3 peaks— can determine the density of CDM  About five times that of the baryon density  23% of the universe today is CDM!!!  Likely composed of one or more species of sub- atomic particles  interact very weakly with ordinary matter

Dark Energy  However, 72% of critical density is unspecified…..  Lets call the leftovers Dark Energy  Its influence has grown as universe expands \  It explains many observed phenomena

Cosmic Neutrinos (5 year results)  5 year data determines the temperature fluctuations at small angles more precisely  Theoretical prediction of the third peak in the angular power spectrum  Only matches the data if the very early universe was bathed in a vast number of neutrinos which would have smoothed out the density perturbations very slightly.  The neutrino background was first inferred in 2005  But first time measured solely from WMAP data

What Does this Tell Us? Polarization of the CMBR

Polarization  Peaks in angular power spectrum that correspond to small scales should be dampened in specific way  As predicted by standard model of cosmology  Dampening causes radiation to gain polarization  Where dampening occurs (on small scales) photons can travel w/ little scattering  Retain directional information = polarization

Polarization Cont.  Scattered light is often polarized  The electron-photon scattering cross-section depends upon polarization of incoming photon  This effect allows scientist to investigate the properties of the electrons that the photons were scattered off of

Polarization, cont. Image from WMAP website

Constraints on Inflation  From polarization, three year results were able to put tight limitations on the spectral index of the fluctuation (α)  This is the main parameter that inflation describes  Three year results—α<1  Five year results α = ±  Rules out a lot of inflationary models

Constraints on Inflation, cont.  One of the greatest tests of inflation would be to detect gravitational wave relics  If inflation occurred at “grand unification scale”— could be detected by CMBR polarization  Vortex-like pattern created by gravity waves  If α is indeed greater than 0.95, then ratio of the gravitational-wave and density contributions to the CMB anisotropy needs to be greater than 0.01 for inflation to past test  Five Year--Gravity waves no more than 20% to total temperature anisotropy –many models ruled out

Origins of Stars and Galaxies  Ionizing material affects polarization  Provides an idea of when the “cosmic dark ages” ended and the first stars begin to shine  For polarization signal to be as large as we see it—stars need to have started forming earlier than first billion years  Three year results –first stars start to form around 400 million years  Quasars formed later—so universe partially neutral around 1 billion years  “lighting up” probably long process

Even More Parameters

The Age of the Universe  The First peak in the angular power spectrum:  Know acoustic size: r s = 147 ± 2 Mpc  Known redshift: z dec = 1089 ± 1  Then, after determining the geometry of the universe (flat) and CMB light travel time over distance determined by decupling surface (d a = or -0.3 Gpc)…  We find the age of the universe is t 0 = ± 0.12 Gyr (5 year result)

Hubble Constant  We now have determined the age of the universe and matter density  Can use this to determine the Hubble Constant  The five year results find H 0 = 70.1 ± 1.3 km/s/Mpc  This measurement is consistent with the values from the HST Key Project, gravitational lens timing, and measurements of the Sunyaev-Zeldovich Effect

Optical Depth and Reionization  With longer integration of the large-scale polarization anisotropy, there has been a significant improvement in the measurement of the optical depth to reionization  τ = ±  We also know the redshift of reionization z reion = 10.8 ± 1.4  This measurement suggests that the re- ionization of the universe took place very gradually

From CMBR to Galaxy Clusters

The Characteristic Length  Often called the acoustic scale  Distance a point source traveled from just after inflation to decoupling  Hubble expansion has expanded the universe a thousand fold  The radius of that sound sphere is 480 million light years  After decoupling—acoustic scale constant coming separation of 480Mly

Creation of Clustering  Primordial fluctuation seen now as clustering of galaxies  Fluctuations and regions of “over density” were seeds for gravitational wells that grow larger and denser with time.  The real cosmic density is a superposition of spherical wave shells  The spatial correlation of galaxies is still enhanced at a commoving distance corresponding to the size of the shell at decoupling (480 Mlyr)

Mapping Effects of Primordial Sound Wave  Galaxy redshift surveys map out the universe in three dimensions  From this, can map galaxy correlation function  Excess probability of finding one galaxy a particular distance from another

Mapping Effects of Primordial Sound Wave  The peak--the excess probability of finding galaxies 480 Mly from another  Predicted by WMAP  This single peak corresponds to all the harmonic peaks in the CMBR power spectrum. That is the primordial sound wave!!!

Structure Formation Simulation  vxk vxk

Cosmic Distances  Because this length scale of the baryon acoustic peak can be calculated from known physics and quantities, it gives us a cosmic distance scale  The more distant a galaxy is from Earth, the smaller angle the commoving separation subtends on the sky.  By measuring the angular correlations within a large-enough cluster of galaxies, one can determine how far away it is.