Ly$\alpha$ forest power spectrum as an emerging window into the epoch of reionization and cosmic dawn

Conventional wisdom was that thermal relics from the epoch of reionization (EOR) would vanish swiftly. Recently, however, it was shown that these relics can survive to lower redshifts ($z \sim 2$) than previously thought, due to gas at mean density being heated to $T \sim 3 \times 10^4$ K by reionization, which is inhomogeneous, and shocks. Given the high sensitivities of upcoming Ly$\alpha$ forest surveys, this effect will be a novel broadband systematic for cosmological application. From the astrophysical point of view, however, the imprint of inhomogeneous reionization can shed light on the EOR and cosmic dawn. We utilize a hybrid method -- which includes two different simulation codes capable of handling the huge dynamical range -- to show the impact of patchy reionization on the Ly$\alpha$ forest and its dependence on different astrophysical scenarios. We found statistically significant deviations in the 1D Ly$\alpha$ power spectrum at $k = 0.14$ cMpc$^{-1}$ that range from $\sim 1\%$ at $z = 2$ up to almost $\sim 20\%$ at $z = 4$. The deviations in the 3D Ly$\alpha$ power spectrum, at the same wavenumber, are large and range from a few per cent at $z = 2$ up to $\sim 50\%$ at $z = 4$, although these deviations ignore the effect of He II reionization and AGN feedback at $z<4$. By exploiting different $k$-dependence of power spectrum among various astrophysical scenarios, the effect of patchy reionization on the Ly$\alpha$ forest power spectrum can open a new window into cosmic reionization and possibly cosmic dawn.