Higher Curvature Corrections to Primordial Fluctuations in Slow-roll Inflation

TL;DR

This work investigates higher curvature corrections to slow-roll inflation arising from Gauss-Bonnet couplings and parity-violating terms. By formulating a slow-roll framework with five parameters $\epsilon,\eta,\alpha,\beta,\gamma$, it derives how these corrections modify scalar and tensor fluctuations, including a potentially blue tensor spectrum and enhanced tensor-to-scalar ratio $r$, as well as a nonzero circular polarization of primordial gravitational waves. The authors provide analytic expressions for the scalar tilt $n_\psi$, tensor tilt $n_T$, and $r$, and illustrate the impact with chaotic inflation examples where otherwise disfavored models can fit observations. The study highlights observable signatures in B-mode polarization and GW polarization that could point to Gauss-Bonnet and parity-violating physics, linking inflationary phenomenology to possible string-inspired corrections. They also emphasize that GB corrections can be dynamically important for the inflaton despite being energetically subdominant, and outline directions for future work including vector fields and deriving coupling functions from fundamental theories.

Abstract

We study higher curvature corrections to the scalar spectral index, the tensor spectral index, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find that the higher curvature corrections can not be negligible in the dynamics of the scalar field, although they are energetically negligible. Indeed, it turns out that the tensor-to-scalar ratio could be enhanced and the tensor spectral index could be blue due to the Gauss-Bonnet term. We estimate the degree of circular polarization of gravitational waves generated during the slow-roll inflation. We argue that the circular polarization can be observable with the help both of the Gauss-Bonnet and parity violating terms. We also present several examples to reveal observational implications of higher curvature corrections for chaotic inflationary models.

Figures (4)

• Figure 1: Expected spectral index $n_\psi$ and tensor-to-scalar ratio $r$ of the model (\ref{['example']}) are shown. We have also plotted constraints from WMAP 5-year result, combined with BAO and Type I SN. The contours denote 68% and 95% confidence level. We used the out-put from Cosmological Parameters Plotter at LAMBDA lambda. Each line corresponds to the parameter (i) $m=10^{-5}\times M_{\rm Pl}$, $\lambda=0$, $\kappa=0$ (ordinary slow-roll), (ii) $m=10^{-5}\times M_{\rm Pl}$, $\lambda=10^{10}$, $\kappa=0.003$ and (iii) $m=10^{-5}\times M_{\rm Pl}$, $\lambda=10^{10}$, $\kappa=0.01$, from upper to lower, taking $\phi>0$. Blue-colored lines denote the region that generate blue spectrum in tensor modes, and we plot some values of $n_{\rm T}$.
• Figure 2: The tensor to the scalar ratio and the tensor spectral index are plotted. We have also shown the slow-roll parameters. Here we set parameters as $m=10^{-5}\times M_{\rm Pl}$, $\lambda=10^{10}$ and $\kappa=0.003$.
• Figure 3: Expected spectral index $n_\psi$ and tensor-to-scalar ratio $r$ of the model (\ref{['example_2']}) are plotted. The constraints from WMAP 5-year data are also shown. Each line corresponds to the parameter (i) $\Lambda=10^{-14}$, $\lambda=0$, $\kappa=0$ (ordinary slow-roll), (ii) $\Lambda=10^{-14}$, $\lambda=1.5\times10^{10}$, $\kappa=0.1$ and (iii) $\Lambda=10^{-14}$, $\lambda=3.5\times10^{10}$, $\kappa=0.1$, from upper to lower.
• Figure 4: The tensor-to-scalar ratio $r$ and slow-roll parameters of the model (\ref{['v_flat']}) corresponding to scalar spectral index $n_\psi$ are plotted. We set parameters as $V_0=10^{-10}\times M_{\rm Pl}^4$, $\lambda=-10^{11}$ and $\kappa=0.1$.