The evolution of the UV luminosity function of globular clusters in the
  E-MOSAICS simulations
  We present the evolution of the rest-frame ultraviolet (UV) properties of the
globular cluster (GC) populations and their host galaxies formed in the
E-MOSAICS suite of cosmological hydrodynamical simulations. We compute the
luminosities of all clusters associated with 25 simulated Milky Way-mass
galaxies, discussed in previous works, in the rest-frame UV and optical bands
by combining instantaneous cluster properties (age, mass, metallicity) with
simple stellar population models, from redshifts $z=0$ to 10. Due to the rapid
fading of young stellar populations in the UV, most of the simulated galaxies
do not host GCs bright enough to be individually identified in deep Hubble
Space Telescope (HST) observations, even in highly magnified systems. The
median age of the most UV-luminous GCs is $<10$ Myr (assuming no extinction),
increasing to $\gtrsim 100$ Myr for red optical filters. We estimate that these
GCs typically only contribute a few per cent of the total UV luminosity of
their host galaxies at any epoch. We predict that the number density of
UV-bright proto-GCs (or cluster clumps) will peak between redshifts $z=1-3$. In
the main progenitors of Milky Way-mass galaxies, $10$-$20$ per cent of the
galaxies at redshifts $1 \lesssim z \lesssim 3$ have clusters brighter than
$M_{\rm UV} < -15$, and less than $10$ per cent at other epochs. The brightest
cluster in the galaxy sample at $z>2$ is typically $M_{\rm UV} \sim -16$,
consistent with the luminosities of observed compact, high-redshift sources.
