# Geometry & Dynamics of the Universe

## Metric of Space-Time

The observed isotropy of the CMB allows one to determine that the metric of space-time
is the Robertson-Walker metric to approximately the same precision as the observed
isotropy of the CMB (Stoeger, Maartens, & Ellis 1995 - *add references & details*)

## Isotropy of Expansion and Space-Time

One can infer the isotropy of the Hubble expansion of the Universe from the observations
of the CMB. The expansion is isotropic to order one part in 100,000 or better.

## Curvature of Space

One can make plausability arguments about the stability of a universe with large
curvature but with the small curvature fluctuations observed vial the CMB.
However, in the context of plausible models, which can be tested, one can
measure directly the curvature of space though the angular location of the
"acoustic peaks" in the CMB anisotropy power spectrum.
Preliminary results at this time show that the curvature of the Universe is small and consistent with a "flat" = Euclidean geometry. Expressed in terms of the curvature of a
Friedman-Robertson-Walker model the results correspond to a density of
Omega = 0.7 + 1.1 - 0.4.

## Topology of the Universe

It is also possible to learn something about the topological connectedness of the Universe.
(references Costa & Smoot , ....)
Simple topologies examples are: spherical universes, cyclindrical universes, cubical universes
with opposited edges identified or more complicated permutations of the identifications
including twists and inversions or not opposite sides.
It could be that the topology of the Universe is very complicated if quantum gravity and
tunneling were important in the early epochs.

## Rotation & Shear of the Universe

CMB observations allow us to put limits on the shear and vorticity of the Universe.
Typically one can set a general limit on the ratio of the shear or vorticity to the
Hubble expansion rate of about 10^-5.
Specific models can provide better tests.
This means for example that the Universe has rotated less than one second of arc
in the last 10 billion years.
Return to the Science Goals Page

On the Smoot Group page
you can read about the experiments and observations of the CMB such as the
*COBE* satellite and its instruments, the MAX/MAXIMA/BOOMERANG
balloon-borne instrument, and the COBRAS/SAMBA satellite (now approved
by the European Space Agency).

Revised 29 May 1996; smoot@cosmos.lbl.gov