Cmb and the topology of the universe
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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


Cmb and the topology of the universe

How Big is the Observable Universe ?

Relative to the local curvature & topological scales

COSMO-05, Bonn 2005


Dirichlet domain and dimensions of the compact space

Dirichlet domain and dimensions of the compact space

RLS < R<

COSMO-05, Bonn 2005


Dirichlet domain and dimensions of the compact space1

Dirichlet domain and dimensions of the compact space

RLS > R>

COSMO-05, Bonn 2005


Cmb and the topology of the universe

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


Temperature along the correlated circles pure lss signal

Temperature along the correlated circles(pure LSS signal)

COSMO-05, Bonn 2005


Temperature along the correlated circles isw modification

Temperature along the correlated circles (ISW modification)

COSMO-05, Bonn 2005


Cmb and the topology of the universe

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


Complete surface and integrated large angle t t

Complete, surface and integrated large-angle ΔT/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


Likelehood comparison of compact closed versus flat universe with 0 7

Likelehood comparison ofcompact closed versus flat Universe with =0.7

COSMO-05, Bonn 2005


Cmb and the topology of the universe

WMAP: Angular power spectrum

NASA/WMAP science team

COSMO-05, Bonn 2005


Cmb and the topology of the universe

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


Cmb and the topology of the universe

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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