Cosmological Spectral Deconvolution
  One of the main goals of modern observational cosmology is to map the large
scale structure of the Universe. A potentially powerful approach for doing this
would be to exploit three-dimensional spectral maps, i.e. the specific
intensity of extragalactic light as a function of wavelength and direction on
the sky, to measure spatial variations in the total extragalactic light
emission and use these as a tracer of the clustering of matter. A main
challenge is that the observed intensity as a function of wavelength is a
convolution of the source luminosity density with the rest-frame spectral
energy distribution. In this paper, we introduce the method of spectral
deconvolution as a way to invert this convolution and extract the clustering
information. We show how one can use observations of the mean and angular
fluctuations of extragalactic light as a function of wavelength, assuming
statistical isotropy, to reconstruct jointly the rest-frame spectral energy
distribution of the sources and the source spatial density fluctuations. This
method is more general than the well known line mapping technique as it does
not rely on spectral lines in the emitted spectra. After introducing the
general formalism, we discuss its implementation and limitations. This formal
paper sets the stage for future more practical studies.
