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All article from Shape of the Universe, WMAP
website at NASA.
Consideration of the shape of the
universe can be split into two:
local geometry, which relates especially
to the curvature of the universe,
especially in the observable universe
global geometry, which relates to the
topology of the universe as a whole,
measurement of which may not be within
our ability.
Local geometry (spatial
curvature)
• The local geometry is the curvature
describing any arbitrary point in the
observable universe (averaged on a
sufficiently large scale). Many
astronomical observations, such as
those from supernovae and the
Cosmic Microwave Background (CMB)
radiation, show the observable
universe to be very close to
homogeneous and isotropic and infer
it to be accelerating.
arbitrary: random
Homogeneous: same quailty
Isotropy: is uniformity in all orientations
Possible local geometries
• There are three categories for the
possible spatial geometries
of constant curvature, depending on
the sign of the curvature. If the
curvature is exactly zero, then the
local geometry is flat; if it is positive,
then the local geometry is spherical,
and if it is negative then the local
geometry is hyperbolic.
• Under the assumption that the
universe is homogeneous
and isotropic, the curvature of the
observable universe, or the local
geometry, is described by one of the
three "primitive" geometries (in
mathematics these are called
the model geometries):
a. 3-dimensional Flat Euclidean geometry,
generally notated as E3
b. 3-dimensional spherical geometry with
a small curvature, often notated as S3
c. 3-dimensional hyperbolic
geometry with a small curvature
Hyperbolic: exaggerating
Global geometry
• Global geometry covers the geometry,
in particular the topology, of the whole
universe—both the observable universe
and beyond. While the local geometry
does not determine the global
geometry completely, it does limit the
possibilities, particularly a geometry of
a constant curvature. For this
discussion, the universe is taken to be
a geodesic manifold, free of topological
defects; relaxing either of these
complicates the analysis considerably.
• study of global geometry are whether
the universe:
a. Is infinite in extent or, more generally,
is a compact space;
b. Has a simply or non-simply connected
topology.
Infinite: limitless
Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area
of mathematics concerned with the most basic properties of space, such as connectedness.
geodesic is a generalization of the notion of a "straight line" to "curved spaces".
FLRW model of the universe
• In General Relativity, this is modeled
by the Friedmann–Lemaître–
Robertson–Walker (FLRW) model. This
model, which can be represented by
the Friedmann equations, provides a
curvature (often referred to as
geometry) of the universe based on
the mathematics of fluid dynamics, i.e.
it models the matter within the
universe as a perfect fluid. Although
stars and structures of mass can be
introduced into an "almost FLRW"
model, a strictly FLRW model is used
to approximate the local geometry of
the observable universe.
• Another way of saying this is that if all
forms of dark energy are ignored,
then the curvature of the universe can
be determined by measuring the
average density of matter within it,
assuming that all matter is evenly
distributed (rather than the distortions
caused by 'dense' objects such as
galaxies).
How to calculate the shape of the universe
• http://icosmos.co.uk/index.html
Many kinds of universe
1. Flat universe
2. Spherical universe
3. Hyperbolic universe
4. Spherical Expanding Universe
5…….
From Jonathan Strickland
http://science.howstuffworks.
com/dictionary/astronomyterms/space-shape2.htm
Will the Universe expand
forever?
• The fate of the universe is determined by a struggle between the
momentum of expansion and the pull of gravity. The rate of expansion is
expressed by the Hubble Constant, Ho, while the strength of gravity
depends on the density and pressure of the matter in the universe. If the
pressure of the matter is low, as is the case with most forms of matter we
know of, then the fate of the universe is governed by the density. If the
density of the universe is less than the "critical density" which is
proportional to the square of the Hubble constant, then the universe will
expand forever. If the density of the universe is greater than the "critical
density", then gravity will eventually win and the universe will collapse back
on itself, the so called "Big Crunch". However, the results of the WMAP
mission and observations of distant supernova have suggested that the
expansion of the universe is actually accelerating which implies the
existence of a form of matter with a strong negative pressure, such as the
cosmological constant. This strange form of matter is also sometimes
referred to as "dark energy". If dark energy in fact plays a significant role in
the evolution of the universe, then in all likelihood the universe will continue
to expand forever.
http://www.youtube.com/watch?v=kV3
3t8U6w28&feature=related
The video of the shape of the universe
• http://www.youtube.com/watch?v=b3lp0r
LtcMM
http://www.youtube.com/watch?v=9dpqFsIl1dA&fe
ature=related