  Context: CoRoT-2b is one of the most anomalously large exoplanet known. Given
its large mass, its large radius cannot be explained by standard evolution
models. Interestingly, the planet's parent star is an active, rapidly rotating
solar-like star with a large fraction (7 to 20%) of spots. Aims: We want to
provide constraints on the properties of the star-planet system and understand
whether the planet's inferred large size may be due to a systematic error on
the inferred parameters, and if not, how it may be explained. Methods: We
combine stellar and planetary evolution codes based on all available
spectroscopic and photometric data to obtain self-consistent constraints on the
system parameters. Results: We find no systematic error in the stellar modeling
(including spots and stellar activity) that would yield the required ~10%
reduction in size for the star and thus the planet. Two classes of solutions
are found: the usual main sequence solution for the star yields for the planet
a mass of 3.67+/-0.13 Mjup, a radius of 1.55+/-0.03 Rjup for an age that is at
least 130Ma, and should be less than 500Ma given the star's fast rotation and
significant activity. We identify another class of solutions on the pre-main
sequence, in which case the planet's mass is 3.45\pm 0.27 Mjup, its radius is
1.50+/-0.06 Rjup for an age between 30 and 40 Ma. These extremely young
solutions provide the simplest explanation for the planet's size which can then
be matched by a simple contraction from an initially hot, expanded state,
provided the atmospheric opacities are increased by a factor ~3 compared to
usual assumptions for solar compositions atmospheres. Other solutions imply in
any case that the present inflated radius of CoRoT-2b is transient and the
result of an event that occurred less than 20 Ma ago: a giant impact with
another Jupiter-mass planet, or interactions with another object in the system
which caused a significant rise of the eccentricity followed by the rapid
circularization of its orbit. Conclusions: Additional observations of CoRoT-2
that could help understanding this system include searches for infrared excess
and the presence of a debris disk and searches for additional companions. The
determination of a complete infrared lightcurve including both the primary and
secondary transits would also be extremely valuable to constrain the planet's
atmospheric properties and to determine the planet-to-star radius ratio in a
manner less vulnerable to systematic errors due to stellar activity.
