Recent observations from the James Webb Space Telescope revealed a surprisingly large number of galaxies at high redshift, challenging the standard Lambda cold dark matter cosmology with a power-law primordial power spectrum. Previous studies alleviated this tension with a blue-tilted primordial power spectrum [$P(k)\propto k^{m_s}$ with $m_s>1$ at small scales $>1{\mathrm{cMpc}}^{-1}$]. In this study, we examine whether the blue-tilted model can boost dark matter substructures especially at low redshift, thereby addressing other potential challenges to the standard cosmology. First, substructures in the standard cosmological model may not be sufficient to explain the anomalous flux ratio problem observed in strong gravitational lensing. Second, the number of observed nearby satellite galaxies could be higher than the theoretical predictions of the standard cosmology, after completeness correction and tidal stripping by baryonic disks. To study the impact of a blue-tilted primordial power spectrum on substructures, we perform high-resolution cosmological zoom-in dark matter-only simulations of Milky Way host mass halos, evolving to redshift $z=0$. At $z=0$, we find that the blue-tilted subhalo mass functions can be enhanced by more than a factor of 2 for subhalo masses $M_{\mathrm{sub}}\lesssim {10}^{10}{M}_{\odot }$, whereas the subhalo $V_{\max }$ functions can be enhanced by a factor of 4 for maximum circular velocities $V_{\max }\lesssim 30\mathrm{km}/\mathrm{s}$. The blue-tilted scaled cumulative substructure fraction can be an order of magnitude higher at $\sim 10\%$ of the virial radius. The blue-tilted subhalos also have higher central densities, since the blue-tilted subhalos reach the same $V_{\max }$ at a smaller distance $R_{\max }$ from the center. We have also verified these findings with higher-resolution simulations.

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• Cosmology
• Dark matter
• Inflation
• Large scale structure of the Universe
• Astrophysical & cosmological simulations