[\overset{a}{^}_{k}, \overset{a}{^}_{k^{'}}^{†}] = (2 π)^{3} δ^{(3)} (k - k^{'}), [\overset{a}{^}_{k}, \overset{a}{^}_{k^{'}}] = [\overset{a}{^}_{k}^{†}, \overset{a}{^}_{k^{'}}^{†}] = 0.

∣ f_{k} ∣^{2} / a^{2}

∣ k τ ∣ ≪ 1

, and the stated Bunch-Davies vacuum mode and

a = - 1/ (H τ)

give

∣ f_{k} ∣^{2} ≃ \frac{1}{2 k ^{3} τ ^{2}}, \frac{∣ f _{k} ∣ ^{2}}{a ^{2}} = \frac{H ^{2}}{2 k ^{3}} .

The dimensionless power spectrum is consequently

Δ_{δ ϕ}^{2} (k) = \frac{k ^{3}}{2 π ^{2}} \frac{∣ f _{k} ∣ ^{2}}{a ^{2}} = (\frac{H}{2 π})^{2} .

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