Mike's answer is good but there Is more. You can actually see it in the papaer he referred you to, it is an excellent paper. It not only describes the possible sources, but it points to the new physics that it might see. eLisa, also called NGO, will be sensitive to gravitational waves from the early universe (and after), down to 10 to the minus 18 sec after the Big Bang. It will see gravitational waves from merging massive and supermassive black holes going back quite a bit also in time, and so much more sensitively that it will see order of magnitude More details. It will see extra low frequencies which means extra large wavelengths, and so gravitational waves from much bigger cosmological and astrophysical objects.
For instance, it will be sensitive to gravitational waves emitted by cosmological cosmic strings, if they exist. That would be new physics. It will also be sensitive to early universe phase transitions including things like fluctuations for leftover inflation with small bubbles forming,and other major changes in the cosmological history - see the paper. If it finds any of those can also find evidence of higher dimensions in spacetime, and string theory, a huge physics impact if anything is found.
As for black holes, it will probe if tHey behave as general relativity predicts. It'll test the no hair theorem, seeing if mass and spin is all they have, by measuring various multipole moments. Thus, it'll determine if general relativity in the ultra strong regime needs modification or not, or if there are other exotic kinds of matter around that could give them hair (for instant, some scalar or other fields). It'll determine if they can instead be boson stars (Higgs like particles collapsed like neutron stars). It'll be sensitive to significant new physics.
It'll look for other kinds of symmetry breaking like what split the electroweak force into electromagnetic and weak. In the LHC the energies to be reached will be on the order of about 15 TEVs. The grav radiation seen from early times in the universe will include events in the 1000 TEV range.
The sensitivity of eLisa is hugely more than that of Ligo. Mainly because of the much longer interferometer arm lengths, 1 million kilometers vs Ligo's 5 Kms or so. It will see black holes spiraling in to merge for much longer than Ligo. Ligo saw the last 1/4 second of the black hole mergers, at relatively low SNR. eLisa will see supermassive black holes all over the universe spiraling in and then merging up to months before they merge, thus averaging a lot of data. It will see the actual mergers and ring downs much more sensitively than Ligo, so it will be able to see any minor deviation from the predictions of general relativity, in the Strong gravity domain. That will include a lot more detail in the merger phase, and possibly higher order effects describing the dynamics of the merger, and then the ring down. It will determine a lower limit to the mass of the graviton by seeing any dispersion in the speed of the gravitational waves as function of frequency, down to orders or magnitude better than what we know now. It can eliminate various enahncementS or alternative gravity theories that way. It will see gravitational waves from binary neutron stars
It will detect so many supermassive black holes that it will be able to form a history of galactic formation, seeded by those black holes in their centers. It might, but I didn't see any specifics, thus determine some more details one the characteristics of dark matter that is also known to help in Galaxy formation.
I'd didn't see anything in the paper on dark matter or energy. But I did not read it all carefully.
I knew some of this, but the paper opened my eyes to the extraordinary new realm of physics these gravitational observatories open up.
Not bad for just 3 satellites.