The impact of AGN feedback on the 1D power spectra from the Ly$\alpha$
  forest using the Horizon-AGN suite of simulations
  The Lyman-$\alpha$ forest is a powerful probe for cosmology, but it is also
strongly impacted by galaxy evolution and baryonic processes such as Active
Galactic Nuclei (AGN) feedback, which can redistribute mass and energy on large
scales. We constrain the signatures of AGN feedback on the 1D power spectrum of
the Lyman-$\alpha$ forest using a series of eight hydro-cosmological
simulations performed with the Adaptative Mesh Refinement code RAMSES. This
series starts from the Horizon-AGN simulation and varies the sub-grid
parameters for AGN feeding, feedback and stochasticity. These simulations cover
the whole plausible range of feedback and feeding parameters according to the
resulting galaxy properties. AGNs globally suppress the Lyman-$\alpha$ power at
all scales. On large scales, the energy injection and ionization dominate over
the supply of gas mass from AGN-driven galactic winds, thus suppressing power.
On small scales, faster cooling of denser gas mitigates the suppression. This
effect increases with decreasing redshift. We provide lower and upper limits of
this signature at nine redshifts between $z=4.25$ and $z=2.0$, making it
possible to account for it at post-processing stage in future work given that
running simulations without AGN feedback can save considerable amounts of
computing resources. Ignoring AGN feedback in cosmological inference analyses
leads to strong biases with 2\% shift on $\sigma_8$ and 1\% shift on $n_s$,
which represents twice the standards deviation of the current constraints on
$n_s$.
