What is the next step in cosmology

[wolram]

I think gravitational radiation mapping, but this will not happen until we have space based observations, until then we have to rely on LIGO which is in its infancy.

 

[Chalnoth]

Some other possibilities:
1. Detection of primordial B-mode polarization of the CMB.
2. Use of BH-BH mergers as standard (or standardizable) candles. I saw a talk a little while ago where they showed that if we could find an optical signal of the event, and in particular measure its redshift, the BH-BH mergers would be vastly more accurate than supernovae as standard candles. I think we'd need three gravity wave observatories to all detect the same event to have a chance of narrowing the location in the sky sufficiently to point telescopes at it before the light fades, if there is any detectable light at all.
3. Observations of the "dark ages" before the stars turned on through measuring the 21cm Hydrogen line (see here).
4. More accurate and larger galaxy surveys to better nail down dark energy. These will be generally slow, incremental improvements, but still important for better understanding of cosmology.