Small-scale Effects of Thermal Inflation on Halo Abundance at High-$z$,
  Galaxy Substructure Abundance and 21-cm Power Spectrum
  We study the impact of thermal inflation on the formation of cosmological
structures and present astrophysical observables which can be used to constrain
and possibly probe the thermal inflation scenario. These are dark matter halo
abundance at high redshifts, satellite galaxy abundance in the Milky Way, and
fluctuation in the 21-cm radiation background before the epoch of reionization.
The thermal inflation scenario leaves a characteristic signature on the matter
power spectrum by boosting the amplitude at a specific wavenumber determined by
the number of e-foldings during thermal inflation ($N_{\rm bc}$), and strongly
suppressing the amplitude for modes at smaller scales. For a reasonable range
of parameter space, one of the consequences is the suppression of minihalo
formation at high redshifts and that of satellite galaxies in the Milky Way.
While this effect is substantial, it is degenerate with other cosmological or
astrophysical effects. The power spectrum of the 21-cm background probes this
impact more directly, and its observation may be the best way to constrain the
thermal inflation scenario due to the characteristic signature in the power
spectrum. The Square Kilometre Array (SKA) in phase 1 (SKA1) has sensitivity
large enough to achieve this goal for models with $N_{\rm bc}\gtrsim 26$ if a
10000-hr observation is performed. The final phase SKA, with anticipated
sensitivity about an order of magnitude higher, seems more promising and will
cover a wider parameter space.
