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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?)

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

- 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?

- 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

(cosmological constant)

Flat Universe

tot=m+ Λ=1

WMAP

Amount of “matter”

(normal + dark)

Measuring the geometry of the UniverseHOT

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

- 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

Temperature x Polarization

Isotropy

- “isotropy”
- “statistical isotropy”
- scalars: statistical properties determined by distances

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

- 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

- 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?

- 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

- 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 (!)

Priors and Parameters

VSA: Rebolo et al 2004

CMB Power spectra

ℓ(ℓ+1)Cℓ/2π

Mean-square fluctuation power (µK2)

(If isotropic)

(otherwise)

Multipole ℓ~ 180°/angle

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

CBI: Readhead et al

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

- 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

- Just the one-point function (PDF)
- Can also check the 2-point distribution, etc

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

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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