  Baryonic feedback effects lead to a suppression of the weak lensing angular
power spectrum on small scales. The poorly constrained shape and amplitude of
this suppression is an important source of uncertainties for upcoming
cosmological weak lensing surveys such as Euclid or LSST. In this first paper
in a series of two, we use simulations to build a Euclid-like tomographic mock
data-set for the cosmic shear power spectrum and the corresponding covariance
matrix, which are both corrected for baryonic effects following the
baryonification method of Schneider et al. (2019). In addition, we develop an
emulator to obtain fast predictions of the baryonic power suppression, allowing
us to perform a likelihood inference analysis for a standard $\Lambda$CDM
cosmology with both cosmological and astrophysical parameters. Our main
findings are the following: (i) ignoring baryonic effects leads to a greater
than 5$\sigma$ bias on the cosmological parameters $\Omega_m$ and $\sigma_8$;
(ii) restricting the analysis to the largest scales, that are mostly unaffected
by baryons, makes the bias disappear, but results in a blow-up of the
$\Omega_m$-$\sigma_8$ contour area by more than a factor of 10; (iii) ignoring
baryonic effects on the covariance matrix does not significantly affect
cosmological parameter estimates; (iv) while the baryonic suppression is mildly
cosmology dependent, this effect does not noticeably modify the posterior
contours. Overall, we conclude that including baryonic uncertainties in terms
of nuisance parameters results in unbiased and surprisingly tight constraints
on cosmology.
