  Upcoming weak lensing surveys, such as LSST, EUCLID, and WFIRST, aim to
measure the matter power spectrum with unprecedented accuracy. In order to
fully exploit these observations, models are needed that, given a set of
cosmological parameters, can predict the non-linear matter power spectrum at
the level of 1% or better for scales corresponding to comoving wave numbers
0.1<k<10 h/Mpc. We have employed the large suite of simulations from the OWLS
project to investigate the effects of various baryonic processes on the matter
power spectrum. In addition, we have examined the distribution of power over
different mass components, the back-reaction of the baryons on the CDM, and the
evolution of the dominant effects on the matter power spectrum. We find that
single baryonic processes are capable of changing the power spectrum by up to
several tens of per cent. Our simulation that includes AGN feedback, which we
consider to be our most realistic simulation as, unlike those used in previous
studies, it has been shown to solve the overcooling problem and to reproduce
optical and X-ray observations of groups of galaxies, predicts a decrease in
power relative to a dark matter only simulation ranging, at z=0, from 1% at
k~0.3 h/Mpc to 10% at k~1 h/Mpc and to 30% at k~10 h/Mpc. This contradicts the
naive view that baryons raise the power through cooling, which is the dominant
effect only for k>70 h/Mpc. Therefore, baryons, and particularly AGN feedback,
cannot be ignored in theoretical power spectra for k>0.3 h/Mpc. It will thus be
necessary to improve our understanding of feedback processes in galaxy
formation, or at least to constrain them through auxiliary observations, before
we can fulfil the goals of upcoming weak lensing surveys.
