If Tidal Dwarf Galaxies tell something about dark matter and thus about cosmology are they cosmological important objects? To answer this question, one should determine how many of them are produced per merger, and then how many manage to survive. Both simulations and observations may give clues on these issues.
From the simple argument that, at high redshift, tidal collisions should have been numerous, some researchers reached the radical conclusion that most dwarfs in the Universe should have a tidal origin . Since this is rather unlikely, the Cold Dark Matter paradigm, and the hierarchical mass assembly it implies have been questioned .
Analyzing a large set of numerical simulations, we concluded that the formation of TDGs was in fact not a very efficient process in galaxy collisions: specific conditions should be met, such as low impact velocities, up to 250 km s-1, leading to mergers, prograde encounters, mass ratios up to 4:1- excluding minor mergers -, and above all initially extended gas in the parent galaxies . Furthermore, only TDGs located near the tip of the tidal tails are able to survive more than 1 Gyr. The production rate is then about 1 TDG per favorable merger. Even if the merging rate increases with redshift, it would then be unlikely that TDGs contribute more than a few percent to the population of dwarf galaxies. However, the initial parameters of our simulations  are valid for nearby mergers. Simulations of mergers tuned for the distant Universe which in particular assume that the disk of the parent galaxies had a higher gas fraction (up to 50%) and was more turbulent, are presented in Fig. 4. They did not generate the very long tidal tails observed in nearby mergers. However a large number of clumps of matter, with typical masses of 108 - 109 M, initially formed in the disks may be kicked out by the collision. Such objects, once independent, have all the properties expected for TDGs.
Figure 4. TDG formation at high redshift, probed by simulations of clumpy disk galaxies with a high gas fraction (Bournaud et al., 2010, submitted)
If such process is as efficient as these simulations show, the Local Universe should be full of such second generation, dark matter poor, dwarf galaxies. Is it really the case? The distribution of the Local Group dwarf spheroidals on specific planes/circles may suggest that they are old TDGs . Given their location, even the Magellanic Clouds were speculated to have been synthesized in an old merger that built the present-day Andromeda galaxy . However to validate such an hypothesis, one needs to check whether it is consistent with all the other properties expected for TDGs: lack of dark matter, specific star formation and chemical enrichment histories. And what is so far known about the properties of the neighbors of the Milky Way does not really support the tidal hypothesis.
Old TDGs remain to be found, first looking at environments where they are expected to have formed efficiently, i.e. where major mergers have likely occurred. If Early-type galaxies result from major mergers, some of their satellites might be of tidal origin. Fig. 5 presents deep optical images of a nearby elliptical galaxy that revealed the presence of three gas-rich TDG candidates, which have likely formed 2-3 Gyr ago.
Figure 5. Discovery of old TDGs around an elliptical galaxy with the CFHT MegaCam camera. The image was obtained as part of the ATLAS3D survey (Cappellari et al., 2011). The three candidates which have morphologies of dEs but are gas-rich - see the bottom g-band images with contours of the HI emission from the WSRT (Serra et al., in prep.) superimposed - lie along a 160 kpc long tidal tail, visible on the top image, where low surface brightness features have been enhanced. The merger has an estimated age of 2-5 Gyr (Duc et al., 2011, submitted)
Such systematic census of old TDGs, coupled with new numerical simulations of mergers, with a proper treatment of the gas and star-formation, should be pursued to determine the real numerical importance of tidal dwarfs.
Acknowledgements I wish to thank all my collaborators, observers and simulation experts, in particular Frédéric Bournaud, Pierre-Emmanuel Belles, Médéric Boquien, Elias Brinks, Ute Lisenfeld, Jonathan Braine, Peter Weilbacher, Etienne Ferriere and Daniel Miralles. The ATLAS3D team, in particular Paolo Serra, is thanked for providing the data shown in Fig. 5. Many thanks to Polis Papaderos for the initiative and organization of this symposium.