COSMO
In the literature: open
Is primordial local non-Gaussianity of order one?
In plain words
If only one field drove inflation, the primordial ripples should be almost perfectly bell-curve distributed. Several fields would leave a measurable correlation between large and small ripples.
Precise statement
Measure the local bispectrum amplitude $f_{\mathrm{NL}}^{\mathrm{local}}$; Planck 2018 gives $f_{\mathrm{NL}}^{\mathrm{local}} = -0.9 \pm 5.1$. Single-field inflation predicts $\left|f_{\mathrm{NL}}^{\mathrm{local}}\right| \ll 1$ in the squeezed limit; many multi-field models give $\left|f_{\mathrm{NL}}^{\mathrm{local}}\right| \ge 1$. An answer is $f_{\mathrm{NL}}^{\mathrm{local}}$ with sigma below 0.5 from scale-dependent galaxy bias and CMB.
What would settle it
SPHEREx and Rubin scale-dependent bias measurements combined with CMB bispectra.