We perform a discrete wavelet analysis of the COBE-DMR 4yr sky maps and find a significant scale-scale correlation on angular scales from about 11 to 22 degrees, only in the DMR face centered on the North Galactic Pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22 degrees, or the standard inflation plus cold dark matter paradigm is ruled out at the > 99% confidence level.Most attempts at quantifying the non-Gaussianity in the cosmic microwave background radiation are motivated by the belief that non-Gaussianity can distinguish inflationary models of structure formation from topological models. While standard inflation predicts a Gaussian distribution of anisotropies [1], spontaneous symmetry breaking produces topological defects whose networks create non-Gaussian patterns on the microwave background radiation on small scales [2]. Minute non-Gaussian features can however be generated by gravitational waves [3] or by the Rees-Sciama [4] and Sunyaev-Zeldovich effects.It is generally held that cosmic gravitational clustering can be roughly described by three régimes: linear, quasilinear, and fully developed nonlinear clustering. Whilst quasi-linear and non-linear clustering induce non-Gaussian distribution functions, if the initial density perturbations are Gaussian, scale-scale correlations and other non-Gaussian features of the density field can not be generated during the linear régime. Hence the linear régime is best suited to study the primordial non-Gaussian fluctuations. Since the amplitudes of the cosmic temperature fluctuations revealed by COBE are as small as ∆T /T 10 −5 , the gravitational clustering should remain in the linear régime on scales larger than about 30 h −1 Mpc and at redshifts higher than 2. Current limits on non-Gaussianity from galaxy surveys probe redshifts smaller than about 1 [5]. Interestingly, at redshifts between 2 and 3, and scales on the order of 40 to 80 h −1 Mpc, there are positive detections of scale-scale correlations in the distribution of Lyα absorption lines in quasar spectra [6]. These clouds are likely to be pre-collapsed and continuously distributed intergalactic gas clouds, and are therefore fair tracers of the cosmic density field, especially on large scales [7]. This may indicate that the primordial fluctuations are scale-scale correlated.While on small angular scales ( 150) there may be some indications of non-Gaussianity [8], studies by traditional non-Gaussian detectors have concluded that there is no evidence of non-Gaussianity in the cosmic temperature fluctuations on large scales [9]. (See however [10].) This does not rule out the existence of scale-scale correlations. Because each non-Gaussian feature is non-Gaussian in its own way, there is no single statistical indicator for ...
Recently, it has been found that the field traced by QSO's Lyα forests is intermittent on small scales. Intermittent behavior is essential for understanding the statistics and dynamics of cosmic gravitational clustering in the nonlinear regime. The most effective method of describing intermittency uses the structure functions and the intermittent exponent, which measure the scale-and order-dependencies of the ratio between the higher order to second order moments of the field. These properties can be used not only to confirm the non-gaussianity of fields, but also to detect the type of non-gaussianity.In this paper, we calculate the structure function and intermittent exponent of 1.) Keck data, which consists of 28 high resolution, high signal to noise ratio (S/N) QSO Lyα absorption spectra, and 2.) Lyα forest simulation samples produced via the pseudo hydro scheme for the low density cold dark matter (LCDM) model and warm dark matter (WDM) model with particle mass m W = 300, 600, 800 and 1000 eV. Aside from the WDM model with m W = 300 eV, the simulation samples are in agreement with observations in the context of the power spectrum. We find, however, that the intermittent behavior of all the simulation samples is substantially inconsistent, both quantitatively and qualitatively, with the Keck data. Specifically, 1.) the structure functions of the simulation samples are significantly larger than that of Keck data on scales k ≥ 0.1 km −1 s, 2.) the intermittent exponent of the simulation samples is more negative than that of Keck data on all redshifts considered, 3.) the order-dependence of the structure functions of simulation samples are closer to the intermittency of hierarchical clustering on all scales, while the Keck data are closer to a lognormal field on small scales. These differences are independent of noise and show that the intermittent evolution modeled by the pseudo-hydro simulation is substantially different from observations, even though they are in good agreement with each other in terms of second and lower order statistics. This result also shows that "weakly" clustered samples, like high resolution Lyα absorption spectrum, are effective in testing dynamical models of structure formation if their intermittent features are considered.Subject headings: cosmology: theory -large-scale structure of the universe
It is of fundamental importance to determine if and how hierarchical clustering is involved in large-scale structure formation of the universe. Hierarchical evolution is characterized by rules which specify how dark matter halos are formed by the merging of halos at smaller scales. We show that scale-scale correlations of the matter density field are direct and sensitive measures to quantify this merging tree. Such correlations are most conveniently determined from discrete wavelet transforms. Analyzing two samples of Lyα forests of QSO's absorption spectra, we find significant scale-scale correlations whose scale dependence is typical for branching processes. Therefore, models which predict a "history" independent evolution are ruled out and the halos hosting the Lyα clouds must have gone through a "history" dependent merging process during their formation.
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