X What is the shape of our universe? By Sandro Berndt.

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What is the shape of our universe?What is the shape of our universe?

By Sandro BerndtBy Sandro Berndt

22What is the shape of our universe?

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Historic views

Theory / Topology

CMB data

Introduction Introduction

Historic views on the universeHistoric views on the universe Theory / TopologyTheory / Topology What CMB tells usWhat CMB tells us


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Historic views

Theory / Topology

CMB data

GeocentricGeocentric

Heliocentric Heliocentric

(~1543)(~1543)

KeplerianKeplerian

(~1606)(~1606)

Early modelsEarly models

[2][3]


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Historic views

Theory / Topology

CMB data

Steady state modelSteady state model

Based on the Based on the perfect cosmological principleperfect cosmological principle

(Universe looks the same from every place and at every time)(Universe looks the same from every place and at every time)

Expansion of the universe fixed by “creation of mass”Expansion of the universe fixed by “creation of mass”

[2]


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Historic views

Theory / Topology

CMB data

Einstein‘s Einstein‘s contributioncontribution

Theory of general relativity Theory of general relativity ↔ shape of the universe↔ shape of the universe

GRT leads to expansion and / or collapseGRT leads to expansion and / or collapse Cosmological constant Cosmological constant ΛΛ introduced as a mathematical fix introduced as a mathematical fix

Different solutions for GRTDifferent solutions for GRT

[2]


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Historic views

Theory / Topology

CMB data

ToposTopos = places = places Defined on a set Defined on a set ConnectionsConnections of subsets / of subsets /

elementselements Topology determines geometryTopology determines geometry Imagination limited to three Imagination limited to three

dimensionsdimensions

TopologiesTopologies

[4]


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Historic views

Theory / Topology

CMB data

Flat geometry: Flat geometry: Simple “parallel transport”Simple “parallel transport” Sum of angles in a triangle 180°Sum of angles in a triangle 180°

Connect opposite sides

Connect circles

TopologiesTopologies


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Historic views

Theory / Topology

CMB data

Torus represents a flat Torus represents a flat geometrygeometry

Finite volumeFinite volume

Torus constructionTorus construction

[3]


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Historic views

Theory / Topology

CMB data

Creatures living in a 1-d worldCreatures living in a 1-d world

22ndnd dimension cannot be realized by inhabitants of the “line” dimension cannot be realized by inhabitants of the “line” No “footsteps” in 1-dNo “footsteps” in 1-d

x x x x x x ???

Low dimensional examples ILow dimensional examples I


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Historic views

Theory / Topology

CMB data

Low dimensional examples IILow dimensional examples II

Creatures in a “plane” worldCreatures in a “plane” world No movement in the 3No movement in the 3rdrd dimension dimension

x x x

x x ???


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Historic views

Theory / Topology

CMB data

What about us?What about us?

““Shortcut” through 4Shortcut” through 4thth dimension dimension

would not be traceablewould not be traceable

x x

???


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Historic views

Theory / Topology

CMB data

The edge of our universeThe edge of our universe

Faces are connectedFaces are connected No end / edge detectableNo end / edge detectable

(Like flat earth turned out to be spheric)(Like flat earth turned out to be spheric)


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Historic views

Theory / Topology

CMB data

Our Galaxy

A hall of mirrors?A hall of mirrors?

Similar to Olbers paradoxSimilar to Olbers paradox Solved by Solved by

redshift redshift size of the universesize of the universe lifetime of stars / galaxieslifetime of stars / galaxies


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Theory / Topology

CMB data

Astronomers Arno Penzias & Robert Wilson Astronomers Arno Penzias & Robert Wilson (Nobel Prize in 1978)(Nobel Prize in 1978)

Isotropic radiation ~ 2.7 KelvinIsotropic radiation ~ 2.7 Kelvin Leftover from hotter and smaller universeLeftover from hotter and smaller universe Supports Big Bang theory Supports Big Bang theory

Discovery in 1964Discovery in 1964

[1]


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Theory / Topology

CMB data

1989 - 1993 1989 - 1993 Detailed view of CMBDetailed view of CMB Explored age / geometry / composition of the universeExplored age / geometry / composition of the universe Supports flat universeSupports flat universe

Cosmic background explorer (COBE)Cosmic background explorer (COBE)

[1]


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Historic views

Theory / Topology

CMB data

T = 2.725 KT = 2.725 K Perfect blackbodyPerfect blackbody

Cosmic background explorer (COBE)Cosmic background explorer (COBE)

[1]


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Theory / Topology

CMB data

Launched 2001Launched 2001 22 – 90 GHz / 3.3 -13.6 mm22 – 90 GHz / 3.3 -13.6 mm 20 x resolution of COBE20 x resolution of COBE ΔΔT = 20 - 35 µK T = 20 - 35 µK

Wilkinson Microwave Anisotropy ProbeWilkinson Microwave Anisotropy Probe

[1]


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Theory / Topology

CMB data

Test for model universeTest for model universe

Angular spectrumAngular spectrum

6000

5000

4000

3000

2000

1000

0

Tem

per

atur

e F

luct

uatio

ns

[µ

K2]

Multipole moment l10 100 500 1000

Angular Size2° 0,5° 0,2°90°

closedflat

open

[1]


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Theory / Topology

CMB data

Age: 13.73 Age: 13.73 ± 0.12± 0.12 billion years billion years Flat curvature (within 1 %)Flat curvature (within 1 %) Baryonic matter only ~ 4.6 %Baryonic matter only ~ 4.6 % Dark matter ~ 23.3 %Dark matter ~ 23.3 % Dark energy ~ 72.1 %Dark energy ~ 72.1 %

WMAP resultsWMAP results

[1]


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CMB data

……

WMAP ResultsWMAP Results

[1]


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CMB data

PLANCK launched May 14PLANCK launched May 14thth 2009 2009 Temperature resolution up by factor 3Temperature resolution up by factor 3 Higher angular resolution Higher angular resolution 25 – 1000 GHz receiver25 – 1000 GHz receiver

More information about the oldest structures and their formationMore information about the oldest structures and their formation New physics for “non-baryonic” matterNew physics for “non-baryonic” matter Consistent theory for the beginning of time / spaceConsistent theory for the beginning of time / space New insights if gravitational waves can be detectedNew insights if gravitational waves can be detected

Still to come…Still to come…


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Theory / Topology

CMB data

[1][1] WMAP mission page, WMAP mission page, http://map.gsfc.nasa.govhttp://map.gsfc.nasa.gov

[2][2] http://www.pbs.org/wnet/hawking/universes/html/univ.htmlhttp://www.pbs.org/wnet/hawking/universes/html/univ.html

[3][3] Free online enzyclopedia, Free online enzyclopedia, http://www.wikipedia.dehttp://www.wikipedia.de

[4] Andreas Müller – Astrophysik, [4] Andreas Müller – Astrophysik, http://www.wissenschaft-online.de/astrowissen/http://www.wissenschaft-online.de/astrowissen/

[5] Kurze Einführung in die Kosmologie,[5] Kurze Einführung in die Kosmologie,

http://www.astro.uni-bonn.de/~peter/cosmo_short.pdf http://www.astro.uni-bonn.de/~peter/cosmo_short.pdf

[6] Collected papers of Albert Einstein[6] Collected papers of Albert Einstein

http://www.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdfhttp://www.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_GRelativity_1916.pdf

ReferencesReferences


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Thank you for your attention!Thank you for your attention!


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Historic views

Theory / Topology

CMB data

[1]

X What is the shape of our universe? By Sandro Berndt.

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