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

In low-energy effective string theory, ${\alpha }^{\mathrm{\prime }}$ corrections involve the coupling of the dilaton field to Gauss-Bonnet term. We assume that the dilaton potential is fine tuned so that the dilaton field may oscillate rapidly for a while around the minimum of its potential but the inflation background is not affected. By numerical method, we find that if the dilaton starts to oscillate at the time of about $\sim 60$ e-folds before the end of inflation, ${\alpha }^{\mathrm{\prime }}$ correction may bring unusual oscillations to the inflationary gravitational wave spectrum, which might be measurably imprinted in the CMB B-mode polarization.