  The discovery of planets orbiting at less than 1 au from their host star and
less massive than Saturn in various exoplanetary systems revolutionized our
theories of planetary formation. The fundamental question is whether these
close-in low-mass planets could have formed in the inner disk interior to 1 au,
or whether they formed further out in the planet-forming disk and migrated
inward. Exploring the role of additional giant planets in these systems may
help us to pinpoint their global formation and evolution. We searched for
additional substellar companions by using direct imaging in systems known to
host close-in small planets. The use of direct imaging complemented by radial
velocity and astrometric detection limits enabled us to explore the giant
planet and brown dwarf demographics around these hosts to investigate the
potential connection between both populations. We carried out a direct imaging
survey with VLT/SPHERE to look for outer giant planets and brown dwarf
companions in 27 systems hosting close-in low-mass planets discovered by radial
velocity. Our sample is composed of very nearby (<20pc) planetary systems,
orbiting G-, K-, and M-type mature (0.5-10Gyr) stellar hosts. We performed
homogeneous direct imaging data reduction and analysis to search for and
characterize point sources, and derived robust statistical detection limits. Of
337 point-source detections, we do not find any new bound companions. We
recovered the emblematic very cool T-type brown dwarf GJ229B. Our typical
sensitivities in direct imaging range from 5 to 30 MJup beyond 2 au. The
non-detection of massive companions is consistent with predictions based on
models of planet formation by core accretion. Our pilot study opens the way to
a multi-technique approach for the exploration of very nearby exoplanetary
systems with future ground-based and space observatories.
