NON-GAUSSIAN TEMPERATURE-FLUCTUATIONS IN THE COSMIC MICROWAVE BACKGROUND SKY FROM A RANDOM GAUSSIAN DENSITY FIELD

We point out that the cosmic microwave background (CMB) temperature fluctuations, observed in the microwave sky with a large antenna beam, may not be Gaussian distributed, even if the primordial matter density fluctuations constitute a random Gaussian field. This effect is due to a dominance of low-order multipoles of the CMB anisotropy pattern and is then relevant for galaxy formation models with large-scale power, which produce CMB angular anisotropies through the familiar Sachs-Wolfe effect. We focus on the most popular case of a flat universe with scale-invariant, Gaussian distributed density fluctuations. In this case 30% of the cosmic observers would reject the hypothesis that CMB temperature fluctuations in their own microwave sky are Gaussian distributed at least at the 99% confidence level. We also give numerical bounds, at the 95% confidence level, for the skewness and kurtosis of the sky pixel temperature fluctuation distribution: these bounds will possibly be useful in discriminating against scenarios with primordial, Gaussian density fluctuations.