Concordance cosmological isotropy gaussianity and the cmb or is the universe boring
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Concordance, Cosmological isotropy, Gaussianity and the CMB (or, is the Universe boring?). Andrew Jaffe Open Questions in Cosmology August 2005. Outline. Relationship between Physical processes Cosmological Parameters Power Spectra Higher-order Correlations Maps. The Physics of the CMB.

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Concordance cosmological isotropy gaussianity and the cmb or is the universe boring

Concordance,Cosmological isotropy, Gaussianity and the CMB(or, is the Universe boring?)

Andrew Jaffe

Open Questions in Cosmology

August 2005


  • Relationship between

    • Physical processes

    • Cosmological Parameters

    • Power Spectra

    • Higher-order Correlations

    • Maps

The physics of the cmb
The Physics of the CMB

  • As Universe cools, p+e  H, when kT=0.3 eV~13.6 eV [400,000 yrs]Sound horizon at LSS ~1°Very rapid transitionionized  neutral, opaque  transparent

W. Hu

What affects the cmb temperature
What affects the CMB temperature?

  • Initial temperature (density) of the photons

  • Doppler shift due to movement of baryon-photon plasma

  • Gravitational red/blue-shift as photons climb out of potential wells or fall off of underdensities

  • Photon path from LSS to today

  • All linked by initial conditions ⇒ 10-5 fluctuations



Measuring curvature with the cmb




Last Scattering Surface

Measuring Curvature with the CMB

Measuring curvature with the cmb1




Last Scattering Surface

Measuring Curvature with the CMB

Measuring curvature with the cmb2




Last Scattering Surface

Measuring Curvature with the CMB

Power spectrum of fluctuations

Mean square fluctuation amplitude

~180°/Angular scale

Power Spectrum of fluctuations

Measuring the geometry of the universe

Amount of “dark energy”

(cosmological constant)

Flat Universe

tot=m+ Λ=1


Amount of “matter”

(normal + dark)

Measuring the geometry of the Universe

Cmb polarization generation






CMB Polarization:Generation

  • Ionized plasma + quadrupole radiation field:

    • Thomson scattering⇒polarized emission

  • Unlike intensity, only generated when ionization fraction, 0<x<1 (i.e., during transition)

  • Scalar perturbations: traces ~gradient of density (like velocity)

Cmb polarization e b decomposition
CMB Polarization: E/B Decomposition

  • 2-d (headless) vector field on a sphere

  • Spin-2/tensor spherical harmonics

  • grad/scalar/E + curl/pseudoscalar/B patterns

  • NB. From polarization pattern⇒ E/B decomposition requires integration: non-local

    • (data analysis problems)






Temperature x Polarization


  • “isotropy”

  • “statistical isotropy”

    • scalars: statistical properties determined by distances

Generating anisotropy
Generating anisotropy

  • Anisotropy in the standard model

    • Local physics

    • Bad luck

  • Beyond the standard model

    • Bianchi models

    • Global topology

    • Generally require coincidences of scales


  • Standard lore:

    • nearly scale-free primordial adiabatic* perturbations in growing mode distributed as a Gaussian (e.g., inflation)

      • Coherent oscillations

    • Small fluctuations (~10-5) prior to last scattering

      • Linear theory

    • Free-streaming since last scattering

    • ⇒ Gaussian, linear CMB(*Large isocurvature fractions allowed — but ~little large qualitative effect on parameters, esp w/ Polarization, LSS, H0 — Moodley, Dunkley, Skordis, Ferreira)

Gaussianity anisotropy
Gaussianity & Anisotropy

  • Gaussian, isotropic, linear fluctuations in potential⇒ Gaussian, isotropic, linear CMB

  • distribution only depends on l

  • methodology: this distribution is the maximum-entropy (minimum information) distribution for an isotropic field

  • Distinction between non-Gaussianity and anisotropy depends on information about the sky signal (e.g., hot/cold spots)

A standard cosmological model
A Standard Cosmological Model?

  • Concordance Cosmology (Ostriker & Steinhardt 1995)

    • Moderate H0, low matter density

  • Acceleration from SNIae

  • Flat Universe from CMB

    • Bond & Jaffe; Knox & Page

    • Clinched by Maxima/Boomerang etc

  • Strong measurements of other parameters: WMAP


  • Largely confirms results from COBE, MAXIMA, BOOMERANG, etc.

    • Flat Universe (=1)

      • 23% Dark Matter

      • 4% Normal Matter

      • 73% “Dark Energy”/Quintessence/Λ (accelerating the expansion)

    • Initial seeds consistent w/ Inflation

    • Hubble constant 72 km/s/Mpc

  • Also some hints of new science:

    • first objects at 200 Million Years

  • Depends on

    • Parameterization

    • prior information

    • other data

    • data analysis methods (!)

Parameters of the standard model
Parameters of the standard model

  • Not independent

  • CMB alone ~5 parameters

Spergel et al

Priors and parameters
Priors and Parameters

VSA: Rebolo et al 2004

Cmb power spectra
CMB Power spectra


Mean-square fluctuation power (µK2)

(If isotropic)


Multipole ℓ~ 180°/angle

The distribution of power spectra
The distribution of power spectra


“# of sigma”

Multipole ℓ~ 180°/angle

Ee te spectra measurements
EE, TE Spectra:Measurements

  • Confirms nearly scale-invariant adiabatic perturbations (inflation), detailed parameters.

    • reionization bump:

    • τ = 0.17 ± 0.04 due tozrec = 20 ± 5


CBI (Readhead et al 04)

DASI (Leitch et al 04)

Polarization measurements
Polarization measurements

CBI: Readhead et al


  • Low quadrupole

    • (cf DMR)

      • +Niarchou et al

  • Aligned multipoles

    • (+Tegmark et al,Land & Magueijo, …)

    • “Unlikely” distribution of low-lalm…

    • Bianchi models?

Higher order moments
Higher-order moments

  • Local model:

  • WMAP: -58 < fNL < 134 (2σ) [Komatsu et al]

    • From map statistics & higher-order moments

    • (cf. inflation: |fNL|~1)

  • NB. Non-Gaussian statistics not independent

Magueijo & Madeiros

Wmap map statistics
WMAP map statistics

  • Just the one-point function (PDF)

    • Can also check the 2-point distribution, etc

Everything is non gaussian
Everything is non-Gaussian

  • The answer depends on the question

    • astro-ph/0405341 “Detection of a non-Gaussian Spot in WMAP”, M. Cruz, E. Martinez-Gonzalez, P. Vielva, L. Cayon

    • astro-ph/0404037 “The Hot and Cold Spots in the WMAP Data are Not Hot and Cold Enough”, D. L. Larson, B. D. Wandelt

  • The more averaging, the more “consistent”

    • Parameters ⇒ spectra ⇒ maps

    • (central limit theorem, not physics)

  • The fewer numbers, the more we expect deviations

  • Biases?

    • for standard spectra

    • For interesting non-gaussianity


  • Robust broad outlines of standard model

    • Within adiabatic, power-law, isotropic context:

    • Flat, accelerating, scale-free, non-baryonic CDM

    • ~early first objects?

  • Sensitive (pixel) measurements of CMB Intensity

    • Beginning to be dominated by systematics?

  • Statistical measurements of polarization

  • Inconsistencies due to physics or small statistics?