We suggest a general relation between the position of the cosmic microwave background temperature power spectrum peaks and the inflationary slow roll parameter $��$. 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.

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