By: Tony Strazzara

Why might our universe be finite? medieval philosophers gave the first

logical arguments supporting a finite universe

during the early 20th century, Einstein proposed a closed, static universe shaped like a hypersphere

in 1929, Edwin Hubble discovers constant rate of expansion of universe

Galaxy clusters slowly growing farther apart If distance between them is increasing today,

then they were closer together in the past Raisin bread analogy Roughly 13.7 billion years ago

Discovered accidentally in 1964 by two radio astronomers, the CMB is electromagnetic radiation filling the universe

Photons emitted from hydrogen plasma roughly 300,000 years after the big bang occurred

Thermal spectrum of ~2.725 K

The surface of last scattering (LSS) Observing the CMB means looking back in

time Looking every direction at one instant in time

produces a sphere

COBE – Cosmic Background Explorer launched November 1989 DMR (differential microwave radiometer)

used to map cosmic radiationWMAP – Wilkinson Microwave

Anisotropy Probe launched June 2001 mission: to determine the content,

evolution and geometry of the universe

Colors Contrast in

clarityShape of data

Temperature fluctuations Large angular scales

Small and infinite universe ~ 70 billion light

years across Let’s change

gears…

A manifold is a space that on a local scale resembles Euclidean geometry of a specific dimension while on a global scale may be more complicated What is a 2-manifold? 3-manifolds

Cosmologists consider only 3 types of geometries for our universe: hyperbolic (negative curvature), elliptic (positive curvature), and Euclidean (zero curvature)

The Hyperbolic Plane

What is a 3-torus?To an observer, line of sight straight

ahead eventually leads to seeing the back of one’s own head

And looking up or the right?We’ll take a look later…

No – data of CMB from COBE disproves a cubic 3-torus (T3 space)

In fact, cosmologists have ruled out the possibility of any toroidal model T1 and T2 spaces

T1 spaceT2 space

T3 space

Due to the nature of most other 3-manifolds, our universe is presumably negatively curved

Cosmologists can propose a topology for the universe, deduce what the CMB should look like, then observe how well COBE/WMAP data matches up So how does this data “match up”?

If observed space (LSS) is larger than physical space, expect correlations in CMB Balloon-cube analogy

Correlation is in form of circle pairs 2 identical circles – one from sphere leaving

a face of the manifold and one from sphere entering opposite face back into the manifold

Seen as 2 circles with identical variations in temperature fluctuations

Think about it first in a 2-manifold… Torus

Now for a 3-manifold… 3-Torus

Distance between points in a circle pair is a path Note – if you choose the same point in both circles,

one as a starting point of the path and the other as the ending point, you have constructed a loop! Why?

By constructing loops in the fundamental group, we can predict the topology of the universe

Distortion due to a negatively curved universe The lines that light follow in hyperbolic space

Circles in the sky will be distorted into ovals because of this curvature of space

PDS is a possible manifold for topology of universe 12 faced polyhedron Each face is a pentagon Glue opposite faces to each other with a minimal

clockwise turn

New evidence supporting the possibility Temperature fluctuations around 12 dodecahedrally spaced circles of radius ~11 degrees found in WMAP correspond unusually well dodecahedrally - phase shift of 36 degrees

Would mean universe has slightly positive curvature

3-TorusMirrored Dodecahedron Poincare Dodecahedron

7-year map released earlier this yearNeutrinosZero curvature

Cornish, Neil J., Spergel, David N., and Starkman, Glenn D. “Measuring the Topology of the Universe.” <http://www.pnas.org/content/95/1/82.full.pdf+html>.

Oliveira-Costa, Angelica de, Smoot, George F., and Starobinsky, Alexei A. . “Can the Lack of Symmetry in the COBE/DMR Maps Constrain the Topology of the Universe?” <http://arxiv.org/PS_cache/astro-ph/pdf/9510/9510109v2.pdf>.

Levin, Janna J., Barrow, John D., Bunn, Emory F., and Silk, Joseph. “Flat Spots: Topological Signatures of an Open Universe in COBE Sky Maps.” <http://arxiv.org/PS_cache/astro-ph/pdf/9702/9702242v1.pdf >.

Levin, Janna. “Missing Lorenz-boosted Circles in the Sky.” <http://arxiv.org/PS_cache/astro-ph/pdf/0403/0403036v1.pdf>.

Roukema, Boudewijn F., Lew, Bartosz, Cechowska, Magdalena, Marecki, Andrzej, and Bajtlik, Stanislaw. “A Hint of Poincare Dodecahedral Topology in the WMAP First Year Sky Map.” <http://arxiv.org/PS_cache/astro-ph/pdf/0402/0402608v4.pdf>.

Greason, Michael R. “Cosmic Background Explorer.” <http://lambda.gsfc.nasa.gov/product/cobe/>.

Greason, Michael R. “Wilkinson Microwave Anisotropy Probe.” <http://lambda.gsfc.nasa.gov/product/map/current/>.

Muir, Hazel. “Tantalising Evidence Hints Universe is Finite.” <http://www.newscientist.com/article/dn4250-tantalising-evidence-hints-universe-is-finite.html>.