The effect of baryons on redshift space distortions and cosmic density
  and velocity fields in the EAGLE simulation
  We use the EAGLE galaxy formation simulation to study the effects of baryons
on the power spectrum of the total matter and dark matter distributions and on
the velocity fields of dark matter and galaxies. On scales
$k{\stackrel{>}{{}_\sim}} 4{h\,{\rm Mpc}^{-1}}$ the effect of baryons on the
amplitude of the total matter power spectrum is greater than $1\%$. The
back-reaction of baryons affects the density field of the dark matter at the
level of $\sim3\%$ on scales of $1\leq k/({h\,{\rm Mpc}^{-1}})\leq 5$. The dark
matter velocity divergence power spectrum at
$k{\stackrel{<}{{}_\sim}}0.5{h\,{\rm Mpc}^{-1}}$ is changed by less than $1\%$.
The 2D redshift-space power spectrum is affected at the level of $\sim6\%$ at
$|\vec{k}|{\stackrel{>}{{}_\sim}} 1{h\,{\rm Mpc}^{-1}}$ (for $\mu>0.5$), but
for $|\vec{k}|\leq 0.4{h\,{\rm Mpc}^{-1}}$ it differs by less than $1\%$. We
report vanishingly small baryonic velocity bias for haloes: the peculiar
velocities of haloes with $M_{200}>3\times10^{11}{{\rm M}_{\odot}}$ (hosting
galaxies with $M_{*}>10^9{{\rm M}_{\odot}}$) are affected at the level of at
most $1~$km/s, which is negligible for $1\%$-precision cosmology. We caution
that since EAGLE overestimates cluster gas fractions it may also underestimate
the impact of baryons, particularly for the total matter power spectrum.
Nevertheless, our findings suggest that for theoretical modelling of redshift
space distortions and galaxy velocity-based statistics, baryons and their
back-reaction can be safely ignored at the current level of observational
accuracy. However, we confirm that the modelling of the total matter power
spectrum in weak lensing studies needs to include realistic galaxy formation
physics in order to achieve the accuracy required in the precision cosmology
era.
