  Light scalar and pseudoscalar particles are compelling dark matter
candidates, with a vast running experimental program to discover them. Previous
studies have shown that these light fields can generate sizable isocurvature
perturbations in high scale inflationary models. Thereby, dark matter existence
and cosmic microwave background measurements impose an upper bound on the
inflationary scale. In this work, focusing on the axion case, we point out that
light fields present during inflation can generate important isocurvature
perturbations also in scenarios of low-scale inflation. In our mechanism, the
axion field starts with some non-zero field value during inflation and rolls
along its potential. Since inflation has a different duration in different
patches of the universe, different regions will then have different values of
the axion field, generating cold dark matter isocurvature modes. These modes
are fully correlated with the adiabatic ones and share the same spectral index.
In this scenario, the axion mass determines a lower bound on the Hubble
parameter during inflation.
