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?)

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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


Outline

Outline

  • 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

Cooler

Hotter


Measuring curvature with the cmb

Flat

=1

Us!

Last Scattering Surface

Measuring Curvature with the CMB


Measuring curvature with the cmb1

Closed

1

Us!

Last Scattering Surface

Measuring Curvature with the CMB


Measuring curvature with the cmb2

Open

1

Us!

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

WMAP

Amount of “matter”

(normal + dark)

Measuring the geometry of the Universe


Cmb polarization generation

COLD

HOT

e

v

v

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)

E

B

B

E


Outline

Temperature

Temperature x Polarization


Isotropy

Isotropy

  • “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


Gaussianity

Gaussianity

  • 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


Concordance

Concordance

  • 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

ℓ(ℓ+1)Cℓ/2π

Mean-square fluctuation power (µK2)

(If isotropic)

(otherwise)

Multipole ℓ~ 180°/angle


The distribution of power spectra

The distribution of power spectra

ν=0.03±1.5

“# 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

WMAP

CBI (Readhead et al 04)

DASI (Leitch et al 04)


Polarization measurements

Polarization measurements

CBI: Readhead et al


Anomolies

Anomolies

  • 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


Maps of the cmb

Maps of the CMB


Wmap map statistics

WMAP map statistics

  • Just the one-point function (PDF)

    • Can also check the 2-point distribution, etc


Wmap map statistics1

WMAP map statistics


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


Outline

  • 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


Conclusions

Conclusions

  • 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?


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