21 cm Angular Power Spectrum from Minihalos as a Probe of Primordial Spectral Runnings

Measurements of 21 cm line fluctuations from minihalos have been discussed as a powerful probe of a wide range of cosmological models. However, previous studies have taken into account only the pixel variance, where contributions from different scales are integrated. In order to sort out information from different scales, we formulate the angular power spectrum of 21 cm line fluctuations from minihalos at different redshifts, which can enhance the constraining power enormously. By adopting this formalism, we investigate expected constraints on parameters characterizing the primordial power spectrum, particularly focusing on the spectral index $n_s$ and its runnings $\alpha_s$ and $\beta_s$. We show that future observations of 21 cm line fluctuations from minihalos, in combination with cosmic microwave background, can potentially probe these runnings as $\alpha_s \sim {\cal O}(10^{-3})$ and $\beta_s \sim {\cal O}(10^{-4})$. Its implications to the test of inflationary models are also discussed.