  We present the evolution of galaxy sizes, from redshift 2 to 0, for actively
star forming and passive galaxies in the cosmological hydrodynamical 1003 cMpc3
simulation of the EAGLE project. We find that the sizes increase with stellar
mass , but that the relation weakens with increasing redshift. Separating
galaxies by their star formation activity, we find that passive galaxies are
typically smaller than active galaxies at fixed stellar mass. These trends are
consistent with those found in observations and the level of agreement between
the predicted and observed size - mass relation is of order 0.1 dex for z < 1
and 0.2-0.3 dex from redshift 1 to 2. We use the simulation to compare the
evolution of individual galaxies to that of the population as a whole. While
the evolution of the size-stellar mass relation for active galaxies provides a
good proxy for the evolution of individual galaxies, the evolution of
individual passive galaxies is not well represented by the observed size - mass
relation due to the evolving number density of passive galaxies. Observations
of z \approx 2 galaxies have revealed an abundance of massive red compact
galaxies, that depletes below z \approx 1. We find that a similar population
forms naturally in the simulation. Comparing these galaxies to their z = 0
descendants, we find that all compact galaxies grow in size due to the
high-redshift stars migrating outwards. Approximately 60% of the compact
galaxies increase in size further due to renewed star formation and/or mergers.
