I have a few ideas kicking around, some of them I keep offline but some of my thoughts can be found below. If any of these sound interesting and you would like to hear more about them feel free to contact me.
Stochastic inflation in a BEC
- Goal: Develop a concrete proposal to measure an analog of super-horizon modes and how they decohere.
- Background: There are a number of proposals for BEC analog cosmology, but only recently was an effective description of super-horizon modes in cosmology worked out.
Systematic hamiltonian engineering for quantum simulation
- Goal: Identify a systematic expansion for some quantum simulator where the simulated Hamiltonian is a leading order term.
- Background: See here. This approach is promising because it does not rely on ab initio knowledge of the underlying physics (or in the language of EFTs a UV completion).