Inflation with Gauss-Bonnet Correction and Higgs Potential

TL;DR

This paper investigates inflation driven by a Higgs-like scalar non-minimally coupled to gravity through a Gauss-Bonnet term with a dilaton-like exponential coupling. It derives the modified background equations under slow-roll, defines appropriate slow-roll parameters, and computes the inflationary observables $n_S$ and $r$ for a quartic Higgs potential, using a Taylor expansion and numerical fits to obtain $phi(N)$. Two parameter sets (α, λ) produce observables in agreement with ACT DR6 data for $N oughly 50$–70, with significantly reduced $r$ compared to GR and $n_S$ in the Planck-compatible range; removing the GB term worsens the fit. The analysis also discusses the gravitational-wave propagation speed, finding $c_{GW}$ stays very close to the speed of light during inflation, supporting observational viability of the model.

Abstract

We investigate the cosmological inflation for the Einstein-Hilbert action plus the Higgs potential function and the Gauss-Bonnet term coupled with the Higgs scalar field through a dilaton-like coupling. Then, using the Friedmann-Lemaître-Robertson-Walker metric and considering the appropriate slow-roll parameters, we derive the necessary equations of motion. In the proposed model, since the e-folding integral cannot be easily solved analytically, we first utilize a well-known Taylor expansion. Then, with a certain range of values derived for the model parameters, utilizing a mixture of several diagrams and numerical analysis methods, we obtain results for the tensor-to-scalar ratio and the scalar spectral index that are in good agreement the latest observational data, particularly from ACT DR6, w within the acceptable range of the e-folding values. Also, in the absence of the Gauss-Bonnet term, we find that the inflationary observables are roughly the same as the predictions of the chaotic inflation model.

Figures (5)

• Figure 1: $y(\phi)= \alpha\lambda e^{-\lambda\phi}\phi^{5}/4$ versus $\phi$ for different values of $\alpha$ and $\lambda$ while satisfying condition (\ref{['Condition1']}).
• Figure 3: $N(\phi)$ versus $\phi$ for a fixed value of $\alpha =0.01$ and different values of $\lambda$.
• Figure 5: $\phi(N)$ versus $N$ for fixed value of $\alpha= 0.01$ and $\lambda = 0.48$. For values of $N$ between around $30$ to $80$, the best curve fits analytically.
• Figure 6: The tensor-to-scalar ratio $r$ versus the scalar spectral index $n_{\rm S}^{}$ for two values of $\alpha$ each with corresponding two values of $\lambda$.
• Figure 7: The speed of gravitational waves $c_{_{\rm GW}}$ versus $N$ for two optimal pairs of $\alpha$ and $\lambda$ in the range of $N$ from $30$ to $80$ during inflation.