# Seminar

# Canadian Institute for Theoretical Astrophysics

#### Monday, 9 September 1996 at 3:10PM

#### McLennan Labs, Room 408

## Probing Large Scale Structure using Percolation and Genus Curves

#### Dr. Varun Sahni

#### IUCAA

We study topological properties of large scale structure
in a set of scale free N-body
simulations using the genus and
percolation curves as topological characteristics.
Our results show that as gravitational clustering advances the
density field shows an increasingly pronounced departure from Gaussianity
reflected in the changing shape of the percolation curve and the
changing amplitude and shape of the genus curve.
Both genus and percolation curves differentiate
between the connectedness of overdense and underdense regions
if plotted against the density. When plotted against the filling factor
the percolation curve retains this property as well.
On the other hand, the genus curve shows very little evolution
when plotted against the filling factor.
Its shape is very sensitive to
the spectrum of primordial density fluctuations and may be a useful indicator
of the initial spectrum.
Thus the genus and percolation curves provide
complementary probes of large scale structure topology.
The percolation curve turns out to be a remarkably sensitive
probe of non-Gaussianity and can be used to discriminate
between models of structure formation and the analysis of observational
data such as
galaxy catalogs and MBR maps. The genus curve shows a pronounced decrease
in amplitude caused by phase correlations in the non-linear regime.

Coffee and donuts will be served after the
seminar in the CITA lounge (Rm 1203A)

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