  We present predictions for the cosmic metal budget in various phases of
baryons from redshift z=6-0, taken from a cosmological hydrodynamic simulation
that includes a well-constrained model for enriched galactic outflows. We find
that substantial amounts of metals are found in every baryonic phase at all
epochs, with diffuse intergalactic gas dominating the metal budget at early
epochs and stars and halo gas dominating at recent epochs. We provide a full
accounting of metals in the context of the missing metals problem at z~2.5,
showing that ~40% of the metals are in galaxies, and the remainder is divided
between diffuse IGM gas and shocked gas in halos and filamentary structures.
Comparisons with available observations of metallicity and metal mass fraction
evolution show broad agreement. We predict stars have a mean metallicity of
one-tenth solar already at z=6, which increases slowly to one-half solar today,
while stars just forming today have typically solar metallicity. Our HI column
density-weighted mean metallicity (comparable to Damped Ly-alpha system
metallicities) slowly increases from one-tenth to one-third solar from z=6-1,
then falls to one-quarter solar at z=0. The global mean metallicity of the
universe tracks ~50% higher than that of the diffuse phase down to z~1, and by
z=0 it has a value around one-tenth solar. Metals move towards higher densities
and temperatures with time, peaking around the mean cosmic density at z=2 and
an overdensity of 100 at z=0. We study how carbon and oxygen ions trace the
path of metals in phase space, and show that OIII-OVII lines provide the most
practical option for constraining intergalactic medium metals at z<2.
