  We show that in the Feebly Interacting Massive Particle (FIMP) model of Dark
Matter (DM), one may express the inflationary energy scale $H_*$ as a function
of three otherwise unrelated quantities, the DM isocurvature perturbation
amplitude, its mass and its self-coupling constant, independently of the
tensor-to-scalar ratio. The FIMP model assumes that there exists a real scalar
particle that alone constitutes the DM content of the Universe and couples to
the Standard Model via a Higgs portal. We consider carefully the various
astrophysical, cosmological and model constraints, accounting also for
variations in inflationary dynamics and the reheating history, to derive a
robust estimate for $H_*$ that is confined to a relatively narrow range. We
point out that, within the context of the FIMP DM model, one may thus determine
$H_*$ reliably even in the absence of observable tensor perturbations.
