String Thresholds, Dynamical Gauss--Bonnet Couplings, and Starobinsky Attractors

Abstract

We develop a string-motivated dynamical Gauss--Bonnet completion of Starobinsky inflation. Since a constant Gauss--Bonnet term is topological in four dimensions, observable effects must arise from a modulus, dilaton, or compactification threshold whose value changes during inflation. We formulate the system as a scalar--Gauss--Bonnet effective theory, derive an invariant matching between the threshold-corrected plateau and the leading CMB observables $n_s$, $r$, and the running $\alpha_s \equiv \mathrm d n_s / \mathrm d \ln k$, and impose explicit string and Kaluza--Klein cutoff bounds. Calabi--Yau topology and string threshold amplitudes are used only as microscopic priors for the threshold function; the observable deformation is fixed only after stabilization, trajectory selection, and single-clock matching. In the controlled heavy-modulus regime, a positive matched deformation raises the scalar tilt, lowers the tensor signal, and makes the running mildly less negative. A representative $X_{24}(1,1,2,8,12)$ example illustrates how topological data and an effective threshold response define a quantitative compactification target for the range $\kappa_G \simeq 7 \text{--} 17$, while emphasizing that this is not a direct prediction from a fully stabilized compactification.