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In low-energy effective string theory, $\alpha'$ corrections involve thecoupling of the dilaton field to Gauss-Bonnet term. We assume that the dilatonpotential is fine tuned so that the dilaton field may oscillate rapidly for awhile around the minimum of its potential but the inflation background is notaffected. By numerical method, we find that if the dilaton starts to oscillateat the time of about $\sim 60$ e-folds before the end of inflation,$\alpha^\prime$ correction may bring unusual oscillations to the inflationarygravitational wave spectrum, which might be measurably imprinted in the CMBB-mode polarization.

Oscillation in power spectrum of primordial gravitational wave as a signature of higher-order stringy corrections