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## Inhomogeneity and the Curvature of the Spacelike Cosmos\par

### Christina Sormani

Lehman College, City University of New York

###
Thursday, October 21, 2004

102 Bradley Hall, 4 pm

Tea 3:30 pm, Math Lounge

**Abstract: **
In the Friedman Model of cosmology the spacelike universe is assumed
to have constant sectional curvature so that locally it is curved
like a sphere, Euclidean Space, or hyperbolic space. This assumption
is justified if one assumes that it is a locally isotropic complete
Riemannian manifold. That is, if one assumes that at every point
*p\in M*, there is an *R>0* and a function *F_p* such that the length
of the far side of a geodesic triangle with angle *\theta* at *p* and
adjacent sides of lengths *s,t is given
by **F_p(\theta, s,t)*, then by Schur's
Lemma, *M* has constant sectional curvature. Note that this *F_p*
formula is like having a law of cosines. \par Here we show that if
the space is only locally ``almost" isotropic in the sense which
allows for both the weak and strong gravitational lensing that has
been observed, then the space is close to a space of constant
sectional curvature in the Gromov Hausdorff sense but not in a smooth
sense. We also prove that the formulas for *F_p* are uniformly close
to the corresponding formulas in a space with constant sectional
curvature, thus allowing one to estimate the distance between stars
using formulas based on the Friedman model.

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This talk is advertised as accessible to graduate students.
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