  The space experiment CoRoT has recently detected transits by a hot Jupiter
across the disc of an active G7V star (CoRoT-Exo-2a) that can be considered as
a good proxy for the Sun at an age of approximately 0.5 Gyr. We present a spot
modelling of the optical variability of the star during 142 days of
uninterrupted observations performed by CoRoT with unprecedented photometric
precision. We apply spot modelling approaches previously tested in the case of
the Sun by modelling total solar irradiance variations. To model the light
curve of CoRoT-Exo-2a, we take into account both the photometric effects of
cool spots as well as those of solar-like faculae, adopting solar analogy. Two
active longitudes initially on opposite hemispheres are found on the
photosphere of CoRoT-Exo-2a with a rotation period of 4.522 $\pm$ 0.024 days.
Their separation changes by approximately 80 degrees during the time span of
the observations. From this variation, a relative amplitude of the surface
differential rotation lower than about 1 percent is estimated. Individual spots
form within the active longitudes and show an angular velocity about 1 percent
smaller than that of the longitude pattern. The total spotted area shows a
cyclic oscillation with a period of 28.9 $\pm$ 4.3 days, which is close to 10
times the synodic period of the planet as seen by the rotating active
longitudes. The implications of such results for the internal rotation of
CoRoT-Exo-2a are discussed on the basis of solar analogy. A possible magnetic
star-planet interaction is suggested by the cyclic variation of the spotted
area. Alternatively, the 28.9-d cycle may be related to Rossby-type waves
propagating in the subphotospheric layers of the star.
