Keeping an eye on DBI: power-counting for small-cs cosmology

Inflationary mechanisms for generating primordial fluctuations ultimately compute them as the leading contributions in a derivative expansion, with corrections controlled by powers of derivatives like the Hubble scale over Planck mass: H/Mp. At face value this derivative expansion breaks down for models with a small sound speed, cs, to the extent that cs ≪ 1 is obtained by having higher-derivative interactions like Leff ∼ (∂ Φ)4 compete with …