Cosmic crystallography using short-lived objects – Active Galactic Nuclei
1
Toruń Centre for Astronomy, N. Copernicus University, ul. Gagarina 11, 87-100 Toruń, Poland e-mail: amr@astro.uni.torun.pl
2
Copernicus Astronomy Centre, ul. Bartycka 18, 00-716 Warsaw, Poland
Received:
6
October
2004
Accepted:
5
January
2005
Cosmic crystallography is based on
the principle that peaks in the pair separation histogram (PSH) of objects
in a catalogue should be induced by the
high number of topologically lensed pairs that
are separated by Clifford translations, in excess to “random” pairs
of objects.
Here we present modifications of this
method that successively improve the signal-to-noise ratio
by removing a
large part of the noise and then false signals induced by
selection effects.
Given the transient nature of the most
readily available tracer objects, Active Galactic Nuclei (AGNs),
the former is possible because
a natural filter for removing many of the noise pairs is available:
when counting pairs of objects in order to create PSHs,
only those
with nearly identical redshifts need to be counted.
This redshift filter (a maximum value of 
)
was applied to a
compilation of AGN catalogues. Further noise was removed by
applying a second filter,
a maximum angle
rad, and a minimum number of pairs
to find each “bunch of pairs” (BoP) where the
vectors (in Euclidean comoving space) defined by pairs
are required to be nearly equal,
whereas in the PSH only the lengths must be nearly equal.
These filters reveal significant signals, which, however,
are due to selection effects. A third filter,
a minimum length 
h-1 Mpc
between the (parallel) vectors in a BoP,
is found to effectively remove these selection effect pairs.
After application of
these successive filters,
no significant topological signal was found.
cosmology: observations – cosmological parameters –
galaxies: quasars: general
© ESO, 2005