  We suggest a general relation between the position of the cosmic microwave
background temperature power spectrum peaks and the inflationary slow roll
parameter $\epsilon$. This relation is based on interpreting the variable
setting the position of the peaks as the quantum distance between the end of
inflation and recombination. This distance is determined by the primordial
cosmological Fisher information introduced in arXiv:2002.04294. The
observational constraints set by cosmic microwave background temperature data
lead to a very stringent prediction for the value of the tensor-to-scalar
ratio: $r=0.01 \pm 0.002$. Future polarization data of the cosmic microwave
background should be able to measure this signal and corroborate or discard our
model.
