Running of spectral index and inflationary models of kinetic coupling-corrected Einstein-Gauss-Bonnet gravity

Abstract

In this work, we investigate the running of the spectral index in inflationary models by analyzing the scalar spectral index for generic parameters within non-minimal kinetic coupling-corrected Gauss-Bonnet gravity. Assuming the slow-roll approximation, we calculate and examine key cosmological quantities, explore various forms of the coupling function and scalar potential, and compare the results with observational data. Specifically, we consider three scenarios, first is a small-field inflation potential coupled to a linear coupling function, a power-law potential with a small-field coupling function, and a mutated hilltop inflation model with a linear coupling function. For each scenario, we numerically plot the spectral index $n_s$, the running of the scalar spectral index $\frac{d{n}_s}{d\ln k}$, and the tensor-to-scalar ratio r, and compare the results with current cosmological data. We find that for different values of the parameters κ, ${\xi }_0$, and specific ranges of α and $V_0$, our model exhibits strong compatibility with Planck 2018 TT, TE, EE + lowE + lensing + BK14 + BAO joint data at 68% and 95% confidence levels, as well as BICEP/Keck data, for the $n_s-r$ and $n_s-n_T$ curves. Additionally, we briefly examine the running of the index ${\alpha }_s$ in the proposed class of inflationary models, finding that the results are in perfect agreement with Planck 2018 TT, TE, EE + lowE + lensing + BK14 data, as well as Planck 2018 95% TT + lowE + lensing + BK15 + BAO data.