gravitational waves - What will eLISA be trying to observe?

The first observation is whether gravitation radiation exists as predicted by General Relativity. Evidence from observations of binary neutron stars says it does, but it remains a major unknown.

Gravitational astronomy will be more like listening than looking. Right now I can hear my kids playing upstairs. I can learn a lot about what they are doing just by noting that sound waves are passing, from a particular direction.

We would expect extreme gravitational events to produce particular wave forms, for example black hole mergers should make a "tone" that rises in pitch as the two event horizons merge at faster rates. Again we have lots of theory on this but if we can "hear" these events we can check if GR does correctly model gravity in these situation, or if there is something missing.

Most interesting would be if we do hear Black hole mergers, but they don't sound like what we have expected. That would mean that there is more to gravity than we understand, and would lead to new science.