x What is the shape of our universe? By Sandro Berndt

What is the shape of our universe? x Historic views Theory / Topology CMB data 2 Introduction Historic views on the universe Historic views on the universe Theory / Topology Theory / Topology What CMB tells us What CMB tells us

What is the shape of our universe? x Historic views Theory / Topology CMB data 3 Geocentric Geocentric Heliocentric Heliocentric(~1543) Keplerian Keplerian(~1606) Early models [2][3]

What is the shape of our universe? x Historic views Theory / Topology CMB data 4 Steady state model Based on the perfect cosmological principle Based on the perfect cosmological principle (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]

What is the shape of our universe? x Historic views Theory / Topology CMB data 5 Einstein‘s contribution Theory of general relativity ↔ shape of the universe Theory of general relativity ↔ shape of the universe GRT leads to expansion and / or collapse GRT leads to expansion and / or collapse Cosmological constant Λ introduced as a mathematical fix Cosmological constant Λ introduced as a mathematical fix Different solutions for GRT Different solutions for GRT [2]

What is the shape of our universe? x Historic views Theory / Topology CMB data 6 Topos = places Topos = places Defined on a set Defined on a set Connections of subsets / elements Connections of subsets / elements Topology determines geometry Topology determines geometry Imagination limited to three dimensions Imagination limited to three dimensions Topologies [4]

What is the shape of our universe? x Historic views Theory / Topology CMB data 7 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 Topologies

What is the shape of our universe? x Historic views Theory / Topology CMB data 8 Torus represents a flat geometry Torus represents a flat geometry Finite volume Finite volume Torus construction [3]

What is the shape of our universe? x Historic views Theory / Topology CMB data 9 Creatures living in a 1-d world Creatures living in a 1-d world 2 nd dimension cannot be realized by inhabitants of the “line” 2 nd dimension cannot be realized by inhabitants of the “line” No “footsteps” in 1-d No “footsteps” in 1-d xxx xxx ??? Low dimensional examples I

What is the shape of our universe? x Historic views Theory / Topology CMB data 10 Low dimensional examples II Creatures in a “plane” world Creatures in a “plane” world No movement in the 3 rd dimension No movement in the 3 rd dimension x xx x x ???

What is the shape of our universe? x Historic views Theory / Topology CMB data 11 What about us? “Shortcut” through 4 th dimension “Shortcut” through 4 th dimension would not be traceable x x ???

What is the shape of our universe? x Historic views Theory / Topology CMB data 12 The edge of our universe Faces are connected Faces are connected No end / edge detectable No end / edge detectable (Like flat earth turned out to be spheric)

What is the shape of our universe? x Historic views Theory / Topology CMB data 13 Our Galaxy A hall of mirrors? Similar to Olbers paradox Similar to Olbers paradox Solved by Solved by redshift redshift size of the universe size of the universe lifetime of stars / galaxies lifetime of stars / galaxies

What is the shape of our universe? x Historic views Theory / Topology CMB data 14 Astronomers Arno Penzias & Robert Wilson (Nobel Prize in 1978) Astronomers Arno Penzias & Robert Wilson (Nobel Prize in 1978) Isotropic radiation ~ 2.7 Kelvin Isotropic radiation ~ 2.7 Kelvin Leftover from hotter and smaller universe Leftover from hotter and smaller universe Supports Big Bang theory Supports Big Bang theory Discovery in 1964 [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data Detailed view of CMB Detailed view of CMB Explored age / geometry / composition of the universe Explored age / geometry / composition of the universe Supports flat universe Supports flat universe Cosmic background explorer (COBE) [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 16 T = K T = K Perfect blackbody Perfect blackbody Cosmic background explorer (COBE) [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 17 Launched 2001 Launched – 90 GHz / mm 22 – 90 GHz / mm 20 x resolution of COBE 20 x resolution of COBE ΔT = µK ΔT = µK Wilkinson Microwave Anisotropy Probe [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 18 Test for model universe Test for model universe Angular spectrum Temperature Fluctuations [µK 2 ] Multipole moment l Angular Size 2°0,5° 0,2°90° closed flat open [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 19 Age: ± 0.12 billion years Age: ± 0.12 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 results [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 20 … WMAP Results [1]

What is the shape of our universe? x Historic views Theory / Topology CMB data 21 PLANCK launched May 14 th 2009 PLANCK launched May 14 th 2009 Temperature resolution up by factor 3 Temperature resolution up by factor 3 Higher angular resolution Higher angular resolution 25 – 1000 GHz receiver 25 – 1000 GHz receiver More information about the oldest structures and their formation More information about the oldest structures and their formation New physics for “non-baryonic” matter New physics for “non-baryonic” matter Consistent theory for the beginning of time / space Consistent theory for the beginning of time / space New insights if gravitational waves can be detected New insights if gravitational waves can be detected Still to come…

What is the shape of our universe? x Historic views Theory / Topology CMB data 22 [1]WMAP mission page, [2] [3]Free online enzyclopedia, [4] Andreas Müller – Astrophysik, [5] Kurze Einführung in die Kosmologie, [6] Collected papers of Albert Einstein References

What is the shape of our universe? x Historic views Theory / Topology CMB data 23 Thank you for your attention!

What is the shape of our universe? x Historic views Theory / Topology CMB data 24 [1]