Identify the underlying physics of inflation (inflaton field and potential)
Determine the physical mechanism responsible for the postulated inflationary epoch, including specifying the correct inflaton field and its potential V(φ), or an alternative microphysical account of accelerated early-universe expansion consistent with observations.
References
But there is also bad news. The data we now have, and maybe all the data we will ever have, leave wide open which of the many possible mechanisms — which sort of field φ, and which potential V(φ) — actually occurred. ... we do not know — and we may never know — the underlying physics of inflation.
The questions of its ultraviolet completion, initial conditions, and embedding in a more fundamental theory remain unanswered.
Nevertheless, several fundamental questions such as the nature of dark matter, the initial conditions of the Universe and the physics of inflation etc., remain open.