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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

- Relationship between
- Physical processes
- Cosmological Parameters
- Power Spectra
- Higher-order Correlations
- Maps

- 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

- 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

Flat

=1

Us!

Last Scattering Surface

Closed

1

Us!

Last Scattering Surface

Open

1

Us!

Last Scattering Surface

Mean square fluctuation amplitude

~180°/Angular scale

Amount of “dark energy”

(cosmological constant)

Flat Universe

tot=m+ Λ=1

WMAP

Amount of “matter”

(normal + dark)

COLD

HOT

e

v

v

- 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)

- 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

Temperature x Polarization

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

- 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)

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

- 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)

- 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

- Flat Universe (=1)
- Also some hints of new science:
- first objects at 200 Million Years

- Depends on
- Parameterization
- prior information
- other data
- data analysis methods (!)

- Not independent
- CMB alone ~5 parameters

Spergel et al

VSA: Rebolo et al 2004

ℓ(ℓ+1)Cℓ/2π

Mean-square fluctuation power (µK2)

(If isotropic)

(otherwise)

Multipole ℓ~ 180°/angle

ν=0.03±1.5

“# of sigma”

Multipole ℓ~ 180°/angle

- 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)

CBI: Readhead et al

- Low quadrupole
- (cf DMR)
- +Niarchou et al

- (cf DMR)
- Aligned multipoles
- (+Tegmark et al,Land & Magueijo, …)
- “Unlikely” distribution of low-lalm…
- Bianchi models?

- 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

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

- 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?