Primordial Non-Gaussian Signatures in the Sky

The presence of non-Gaussian features in the CMB radiation maps represents one of the most long-awaited clues in the search for the actual structure of the primordial radiation. These features could shed some light on the non trivial task of distinguishing the real source of the primeval perturbations leading to large scale structure. In the present paper we briefly review recent work towards finding analytical estimates of the three- and four-point correlation functions and of their zero-lag limits, namely, the skewness and kurtosis, respectively. - Contributed talk to appear in the proceedings of "Birth of the Universe & Fundamental Physics", May 18-21, 1994, Rome, Italy.Comment: 4pp; PostScript fil

Superconducting Cosmic Strings

These relics from the early universe could be the answer to many astrophysical conundrums

The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models

We analyze the temperature three--point correlation function and the skewness of the Cosmic Microwave Background (CMB), providing general relations in terms of multipole coefficients. We then focus on applications to large angular scale anisotropies, such as those measured by the {\em COBE} DMR, calculating the contribution to these quantities from primordial, inflation generated, scalar perturbations, via the Sachs--Wolfe effect. Using the techniques of stochastic inflation we are able to provide a {\it universal} expression for the ensemble averaged three--point function and for the corresponding skewness, which accounts for all primordial second--order effects. These general expressions would moreover apply to any situation where the bispectrum of the primordial gravitational potential has a {\em hierarchical} form. Our results are then specialized to a number of relevant models: power--law inflation driven by an exponential potential, chaotic inflation with a quartic and quadratic potential and a particular case of hybrid inflation. In all these cases non--Gaussian effects are small: as an example, the {\em mean} skewness is much smaller than the cosmic {\em rms} skewness implied by a Gaussian temperature fluctuation field.Comment: 18 pages; LaTeX; 4 PostScript figures included at the end of the file; SISSA REF.193/93/A and DFPD 93/A/8

Is the cosmic microwave background really non-Gaussian?

Two recent papers have claimed detection of non-Gaussian features in the COBE DMR sky maps of the cosmic microwave background. We confirm these results, but argue that Gaussianity is still not convincingly ruled out. Since a score of non-Gaussianity tests have now been published, one might expect some mildly significant results even by chance. Moreover, in the case of one measure which yields a detection, a bispectrum statistic, we find that if the non-Gaussian feature is real, it may well be due to detector noise rather than a non-Gaussian sky signal, since a signal-to-noise analysis localizes it to angular scales smaller than the beam. We study its spatial origin in case it is nonetheless due to a sky signal (eg, a cosmic string wake or flat-spectrum foreground contaminant). It appears highly localized in the direction b=39.5, l=257, since removing a mere 5 pixels inside a single COBE beam area centered there makes the effect statistically insignificant. We also test Guassianity with an eigenmode analysis which allows a sky map to be treated as a random number generator. A battery of tests of this generator all yield results consistent with Gaussianity.Comment: Revised to match accepted ApJL version. 4 pages with 2 figs included. Links and color fig at http://www.sns.ias.edu/~max/gaussianity_frames.html or from [email protected]

Cosmic microwave background bispectrum and slow roll inflation

Recent tentative findings of non-Gaussian structure in the COBE-DMR dataset have triggered renewed attention to candidate models from which such intrinsic signature could arise. In the framework of slow roll inflation with built-in non linearities in the inflaton field evolution we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum ${\cal C}_{\ell_1 \ell_2 \ell_3}$ in terms of the slow roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary $\ell_i$ multipole combination. We stress that a real detection of non-Gaussianity in the CMB would imply that an important component of the anisotropies arises from processes {\it other} than primordial quantum fluctuations. We further investigate the behavior of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small-$\ell$'s considered for increasing multipole $\ell$ while the opposite applies for the standard ${\cal C}_{\ell}$'s

Doppler peaks: a fingerprint of topological defects

The fluctuations in the cosmic microwave background (CMB) on large angular scales (> few degrees) are caused by perturbations in the gravitational field via the Sachs--Wolfe effect. On intermediate scales, 0.1^\circ\lsim\theta\lsim 2^\circ, the dominant contribution is due to coherent oscillations in the baryon radiation plasma before recombination. Unless the universe is reionized at some redshift z>50, these oscillations lead to the `Doppler peaks' in the angular power spectrum. In structure formation scenarios based on inflation the position of the first peak is typically at \ell\sim 200, with a height which is 4 -- 6 times that of the Sachs--Wolfe `plateau'. Here we present a corresponding study for perturbations induced by global textures. We find that the first Doppler peak is reduced to an amplitude comparable to that of the Sachs--Wolfe contribution, and that it is shifted to \ell\sim 350. We believe that our analysis can be easily extended to other types of global topological defects and general global scalar fields

CMB Bispectrum from Active Models of Structure Formation

We propose a new method for the numerical computation of the angular bispectrum of the CMB anisotropies arising from active models such as cosmic topological defects, using a modified Boltzmann code. The method, similarly to CMBFAST, does not use CMB sky maps and requires moderate computational power. As a first implementation, we apply our method to a recently proposed model of simulated cosmic strings and find that the observability of the non-Gaussian signal is negligible

Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation

Measuring the three-point correlators of the Cosmic Microwave Background (CMB) anisotropies could help to get a handle on the level of non-Gaussianity present in the observational datasets and therefore would strongly constrain models of the early Universe. However, typically, the expected non-Gaussian signal is very small. Therefore, one has to face the problem of extracting it from the noise, in particular from the `cosmic variance' noise. For this purpose, one has to construct the best unbiased estimators for the three-point correlators that are needed for concrete detections of non-Gaussian features. In this article, we study this problem for both the CMB third moment and the CMB angular bispectrum. We emphasize that the knowledge of the best estimator for the former does not permit one to infer the best estimator for the latter and vice versa. We present the corresponding best unbiased estimators in both cases and compute their corresponding cosmic variances