postscript
Abstract...
Abstract...
2 Cosmic Strings...
The purpose of this talk is to introduce a new statistic Perivolaropoulos (1997) which is
optimized to detect the large scale non-Gaussian coherence induced by late long
strings on CMB maps. The statistical variable to use is the Sample Mean
Diffrence that is the difference of the mean 
between two
large neighbouring regions of CMB maps. I will first briefly review the main
predictions of models for CMB fluctuations. Models based on inflation predict
generically the existence of scale invariant CMB fluctuations with Gaussian
statistics which emerge as a superposition of plane waves with random phases.
On the other hand in models based on defects (for a pedagogic reviews see e.g.
Brandenberger (1992), Perivolaropoulos (1994)), CMB fluctuations are produced by a superposition of seeds and
are scale invariant (Perivolaropoulos (1993a), Allen et al. (1996)) but non-Gaussian
(Perivolaropoulos (1993b), Perivolaropoulos (1993c), Gangui g96(1996), Gott et al. (1990), Moessner, Perivolaropoulos & Brandenberger (1994)). Observations have indicated that the spectrum
of fluctuations is scale invariant Smoot et al. (1992) on scales larger than about
, the recombination scale, while there seem to be Doppler peaks on
smaller scales. These results are consistent with predictions of both inflation
(Bond et al. (1994)) and defect models (Perivolaropoulos (1993b), Allen et al. (1996) and references therein) even
though there has been some debate about the model dependence of Doppler peaks
in the case of defects.
Inflation also predicts Gaussian statistics in CMB maps for both large and
small scales and this is in agreement with Gaussianity tests made on large
scale data so far. On small angular scale maps where the number of superposed
seeds per pixel is small topological defect models predict non-Gaussian
statistics. This non-Gaussianity however depends sensitively on both, the
details of the defect network at the time of recombination 
and on the
physical processes taking place at 
. This large scale coherence can
induce specific non-Gaussian features even on large angular scales. The
question of how Gaussian are the topological defect fluctuations on large
angular scales will be the focus of this talk.
The reason that the defect induced fluctuations appear Gaussian in maps with
large resolution angle is the large number of seeds superposed on each pixel of
the map. This, by the Central Limit Theorem, leads to a Gaussian probability
distribution for the temperature fluctuations 
.
Non-Gaussianity can manifest itself on small angular scales comparable to
minimum correlation length between the seeds.
These arguments have led most efforts for the detection of defect induced
non-Gaussianity towards CMB maps with resolution angle less than 
(Gott et al. (1990), Ferreira & Magueijo (1997), Perivolaropoulos (1993b)). There is however a loophole in these arguments. They
ignore the large scale coherence induced by the latest seeds. Such large scale
seeds must exist due to the scale invariance and they induce certain types of
large scale coherence in CMB maps. This coherence manifests itself as a special
type of non-Gaussianity which can be picked up only by specially optimized
statistical tests. Thus a defect induced CMB fluctuations pattern can be
decomposed in two parts. A Gaussian contribution 
produced mainly by the superposition of seeds on small scales and possibly by
inflationary fluctuations and a coherent contribution 
induced by the latest seeds. The question that we want to address is: What is
the minimum ratio 
of
the last seed contribution on 
over the corresponding
Gaussian contribution that is detectable at the 
to 
level.