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CMB and the Topology of the Universe. Dmitri Pogosyan, UAlberta. With: Tarun Souradeep Dick Bond and: Carlo Contaldi Adam Hincks. Simon White, Garching, last week: Open questions in Cosmology: Is our Universe is finite or infinite? Is its space curved ? ….

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cmb and the topology of the universe
CMB and the Topology of the Universe

Dmitri Pogosyan, UAlberta

With:

Tarun Souradeep

Dick Bond

and:

Carlo Contaldi

Adam Hincks

Simon White, Garching, last week:

Open questions in Cosmology:

Is our Universe is finite or infinite?

Is its space curved ?

….

COSMO-05, Bonn 2005

preferred parameter region tot 1 02 0 02
Preferred parameter region, tot=1.02 ± 0.02

Ωtot=1.01

RLSS/Rcurv=0.3

COSMO-05, Bonn 2005

slide3
How Big is the Observable Universe ?

Relative to the local curvature & topological scales

COSMO-05, Bonn 2005

slide6
Absence of large scale power

COSMO-05, Bonn 2005

NASA/WMAP science team

correlation function of isotropic cmb
Correlation function of isotropic CMB

Oscillations in the angular spectrum

come from this break

COSMO-05, Bonn 2005

perturbations in compact space
Perturbations in Compact space
  • Spectrum has the lowest eigenvalue.
  • Spectrum is discrete, hence statistics in general is anisotropic, especially at large scales.
  • Statistical properties can be inhomogeneous.
  • However, perturbations are Gaussian, and CMB temperature fluctuations are fully described by pixel-pixel correlation matrix CT(p,p’)
  • We implemented general method of images to compute CT(p,p’) for arbitrary compact topology (Bond,Pogosyan, Souradeep, 1998,2002)

COSMO-05, Bonn 2005

pixel pixel correlation with compact topology using method of images bps phys rev d 2000
Pixel-pixel correlation with compact topology (using method of images, BPS, Phys Rev D. 2000)

COSMO-05, Bonn 2005

example of strong correlation on last scattering surface
Example of strong correlation on last scattering surface

These two points on LSS are identical

And so are these

COSMO-05, Bonn 2005

correlated circles after cornish spergel starkman et al 1998 2004
Correlated Circles(after Cornish, Spergel, Starkman et al, 1998,2004)

(Figure: Bond, Pogosyan & Souradeep 1998, 2002)

COSMO-05, Bonn 2005

positive curvature multiconnected universe
Positive curvature multiconnected universe ?

:

Perhaps,

a Poincare dodecahedron “Soccer ball cosmos” ?

COSMO-05, Bonn 2005

isotropic cpp
Isotropic Cpp’

D/RLSS=10

COSMO-05, Bonn 2005

surface term to dt t
Surface term to DT/T

D/RLSS=0.3

COSMO-05, Bonn 2005

variation of the pixel variance
Variation of the pixel variance

D/RLSS=0.3

COSMO-05, Bonn 2005

constraining the models from maps
Constraining the models from maps
  • Complete topological information is retained when comparison with data is done on map level
  • Low res (Nside=16) maps contain most information, although special techniques as circle searching may benefit from finer pixalization. The cost – additional small scale effects which mask topological correlations.
  • Main signal comes from effects, localized in space, e.q on LSS. But even integrated along the line of sight contributions retain signature of compact topology.
  • Orientation of the space (and, possibly, position of observer) are additional parameters to consider. What is the prior for them ?

COSMO-05, Bonn 2005

slide22
WMAP: Angular power spectrum

NASA/WMAP science team

COSMO-05, Bonn 2005

slide23
Single index n:

(l,m) -> n

Diagonal

COSMO-05, Bonn 2005

inadequacy of isotropized c l s a lm cross correlation
Inadequacy of isotropized Cl’s: alm cross correlation

Very small space

Just a bit smaller than LSS

2 3 4 5 6 7 8 9 10

2 3 4 5 6 7 8 9 10

COSMO-05, Bonn 2005

compression to isotropic cls is lossy inhanced cosmic variance of cl s
Compression to isotropic Cls is lossy Inhanced cosmic variance of Cl’s

COSMO-05, Bonn 2005

slide26
Bipolar Power spectrum (BiPS) :A Generic Measure of Statistical Anisotropy

Bipolar multipole index

A weighted average of the correlation function over all rotations

Except for

when

(This slide is provided as a free advertisement for T. Souradeep talk, Wednesday)

COSMO-05, Bonn 2005

conclusions
Conclusions
  • A fundamental question – whether our Universe is finite or infinite –is still open.
  • The region near Otot=1 is rich with possibilities, with negatively or positively curved or flat spaces giving rise to distinct topological choices.
  • Modern CMB data shows that small Universes with V < VLS are failing to describe the temperature maps. Reason – complex correlation are not really observed (in line with circle finding results).
  • This is despite the fact that it is not too difficult to fit the low l suppression of isotropized angular power spectrum.
  • Integrated along the line of sight contribution to temperature anisotropy masks and modifies topology signature. It must be taken into account for any accurate quantitative restrictions on compact spaces.
  • Full likelihood analysis assumes knowledge of the models. Model independent search for statistical anisotropy calls for specialized techniques – see talk on BiPS by Tarun Souradeep on Wednesday.

COSMO-05, Bonn 2005

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