Do wavelets really detect non-Gaussianity in the 4-year COBE data?

We investigate the detection of non-Gaussianity in the 4-year COBE data reported by Pando, Valls-Gabaud & Fang (1998), using a technique based on the discrete wavelet transform. Their analysis was performed on the two DMR faces centred on the North and South Galactic poles respectively, using the Daubechies 4 wavelet basis. We show that these results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations of the data, we calculate unbiased estimates of the skewness, kurtosis and scale-scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity in the DMR-DSMB map at greater than the 99 per cent confidence level, but most of these occur on pixel-pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond $\ell = 40$ from the COBE maps, only one robust detection remains. Moreover, using Monte-Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. We repeat the analysis for the 53+90 GHz coadded COBE map. In this case, after removing $\ell > 40$ multipoles, two non-Gaussian detections at the 99 per cent level remain. Nevertheless, again using Monte-Carlo simulations, we find that the probability of obtaining two such detections by chance is 0.28. Thus, we conclude the wavelet technique does {\em not} yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE data.Comment: 7 pages, 5 figures. Revised version including discussion of orientation sensitivity of the wavelet decomposition. MNRAS submitte

Analytical approach to the transition to thermal hopping in the thin- and thick-wall approximations

The nature of the transition from the quantum tunneling regime at low temperatures to the thermal hopping regime at high temperatures is investigated analytically in scalar field theory. An analytical bounce solution is presented, which reproduces the action in the thin-wall as well as thick-wall limits. The transition is first order for the case of a thin wall while for the thick wall case it is second order.Comment: Latex file, 22 pages, 4 Postscript figure