  Baryonic effects on large-scale structure, if not accounted for, can
significantly bias dark energy constraints. As the detailed physics of the
baryons is not yet well-understood, correcting for baryon effects introduces
additional parameters which must be marginalized over, increasing the
uncertainties on the inferred cosmological parameters. Forthcoming weak lensing
surveys are aiming for percent-level precision on the dark energy equation of
state, so the problem must be thoroughly examined. We use a halo model with
analytic modifications which capture the impact of adiabatic contraction of
baryons and feedback on the matter power spectrum, and generalize the
Navarro-Frenk-White profile to account for a possible inner core. A Fisher
analysis predicts degradations of 40% in the $w_0$-$w_a$ Figure of Merit for a
Euclid-like survey, and up to 80% for other cosmological parameters. We
forecast potential inner core constraints of a few $\mathrm{kpc}$, while for a
fixed inner core, adiabatic concentration and feedback parameters are
constrained to a few percent. We explore the scales where baryons and dark
energy contribute most to the Fisher information, finding that probing to
increasingly non-linear scales does little to reduce degradation. Including
external baryon information improves our forecasts, but limiting degradation to
1% requires strong priors. Adding Planck cosmic microwave background priors
improves the Figure of Merit by a factor of 2.7 and almost completely recovers
the individual marginalized errors on $w_0$ and $w_a$. We also quantify the
calibration of baryon modelling required to reduce biases of dark energy
forecasts to acceptable levels for forthcoming lensing surveys.
