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.