Power Spectra of Slow-Roll inflation in the consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates how the Gauss-Bonnet term influences the primordial power spectra during slow-roll inflation in the novel 4D Einstein-Gauss-Bonnet gravity, providing highly accurate theoretical predictions relevant for future cosmological observations.

Contribution

It offers the first detailed calculation of scalar and tensor spectra with Gauss-Bonnet corrections in 4D Einstein-Gauss-Bonnet gravity, including next-to-leading order slow-roll corrections.

Findings

Most accurate spectral indices and runnings to date.

Second-order corrections significantly impact future measurements.

Compatibility with Planck 2018 constraints for power-law inflation models.

Abstract

The slow-roll inflation which took place at extremely high energy regimes is in general believed to be sensitive to the high-order curvature corrections to the classical general relativity (GR). In this paper, we study the effects of the high-order curvature term, the Gauss-Bonnet (GB) term, on the primordial scalar and tensor spectra of the slow-roll inflation in the consistent $D \to 4$ Einstein Gauss-Bonnet (4EGB) gravity. The GB term is incorporated into gravitational dynamics via the re-scaling of the GB coupling constant $\alpha \to \alpha/(D-4)$ in the limit $ D\to 4$. For our purpose, we calculate explicitly the primordial scalar and tensor power spectra with GB corrections accurate to the next-to-leading order in the slow-roll approximation in the slow-roll inflation by using the third-order uniform asymptotic approximation method. The corresponding spectral indices and their runnings of the spectral indices for both the scalar and tensor perturbations as well as the ratio between the scalar and tensor spectra are also calculated up to the next-to-leading order in the slow-roll expansions. These results represent the most accurate results obtained so far in the literature. In addition, by studying the theoretical predictions of the scalar spectral index and the tensor-to-scalar ratio with Planck 2018 constraint in a model with power-law potential, we show that the second-order corrections are important in future measurements.