Applying wavelet transforms to cosmic microwave background data we probe the statistical nature of primordial density perturbations, in order to learn something about how they were generated. Wavelets are useful tools in such an analysis because they enable the properties of the signal to be studied on different scales, with simultaneous position localization, so that the obscuring effects of the central limit theorem can be reduced. In an independent but complimentary analysis, we derive constraints on the shape of the power spectrum of primordial perturbations, treating it as an arbitrary function, after marginalizing over other cosmological parameters. Here we use wavelets as an efficient tool for the reconstruction and denoising of an unknown function in cosmology.
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