We discuss how one can discriminate models with cold dark matter (CDM) and baryon isocurvature fluctuations. Although current observations such as cosmic microwave background (CMB) can severely constrain the fraction of such isocurvature modes in the total density fluctuations, CMB cannot differentiate CDM and baryon modes by the shape of its power spectra. However, the evolution of CDM and baryon density fluctuations are different for each model, thus it would be possible to discriminate those isocurvature modes by extracting information on the fluctuations of CDM/baryon itself. We discuss that observations of 21 cm fluctuations can in principle differentiate these modes and demonstrate to what extent we can distinguish them with future 21 cm surveys. We show that, when the isocurvature mode has a large blue-tilted initial spectrum, 21 cm survey can clearly probe the difference.Comment: 25 pages, 6 figures, 1 table; (v2) constraints are reanalyzed using a tomography 21cm survey, conclusions unchanged, some references added, accepted for publication in JCA
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