String-inspired Gauss-Bonnet Gravity Inflation and ACT

Abstract

In this article we present a systematic observational verification of the ghost-free string-inspired $f(R,\mathcal{G})$ model, where the Gauss-Bonnet invariant is non-minimally coupled to an auxiliary scalar field $\chi$ through the coupling function $h(\chi )$. Previous studies confirmed the theoretical viability of this framework using phenomenological parameter choices. In this work, for the first time, a systematic comparison with observational data from Planck 2018 and the Atacama Comsology Telescope is carried out via a Bayesian MCMC analysis using the Cobaya code. We explore an extended set of sixteen models constructed from four types of the Hubble parameter combined with power-law, exponential, hybrid, and inverse logarithmic coupling functions $h(\chi )$. The hybrid coupling $h(\chi )=\gamma e^{b_1\chi }{\chi }^{b_2}$, introduced in this context, allows for interpolation between the power-law and exponential forms, providing additional flexibility in controlling the Gauss-Bonnet contribution at different stages of inflation. All sixteen models reproduce the red spectral tilt of scalar perturbations consistent with CMB observations, yielding $n_s\approx 0.97$ at $N=60$ e-folds. We find that the preference for the dataset is systematically determined by the choice of Hubble parametrization rather than by the coupling function. The parameter $\mu \approx 0.1$ remains stable in all configurations, suggesting its fundamental role within the ghost-free formalism.

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