Observational constraints on slow-roll inflation coupled to a Gauss-Bonnet term

We study slow-roll inflation with a Gauss-Bonnet term that is coupled to an inflaton field nonminimally. We investigate the inflationary solutions for a specific type of the nonminimal coupling to the Gauss-Bonnet term and inflaton potential both analytically and numerically. We also calculate the observable quantities such as the power spectra of the scalar and tensor modes, the spectral indices, the tensor-to-scalar ratio, and the running spectral indices. Finally, we constrain our result with the observational data by Planck and BICEP2 experiment.

Figure 1

Left: evolution of the slow-roll parameters $\epsilon$ and ${\delta }_1$ for $\xi (\varphi )={\xi }_0{e}^{-\lambda \varphi }$ with $\lambda =-0.1$. Right: evolution of the slow-roll parameters $\epsilon$ and ${\delta }_1$ for $\xi (\varphi )={\xi }_0{\varphi }^2$.

Figure 2

$e$-folding numbers with $\alpha \equiv \frac{4}{3}{\kappa }^4{V}_0{\xi }_0$ for $V=V_0{\varphi }^2,\xi ={\xi }_0{\varphi }^2$ (solid line) and $V=V_0{\varphi }^4,\xi ={\xi }_0{\varphi }^4$ (dashed line).

Figure 3

Attractor-type solutions of the background equations of motion for standard inflation without the Gauss-Bonnet term, chaotic inflation with the monomial Gauss-Bonnet coupling, and chaotic inflation with the inverse monomial Gauss-Bonnet coupling

Figure 4

Marginalized joint 68% and 95% CL regions for ($n_s$, $r$), using observational data sets with and without a running spectral index, compared to the theoretical prediction of the model (73) with $n=1$. The black dashed line is for the case where model parameter $\alpha =0$ while gray and brown are for the case where $\alpha =-0.003$ and $\alpha =0.001$, respectively. The pairs of red and green dots represent the number of $e$-folds, $N=50$ and $N=60$, respectively.

Figure 5

Marginalized joint 68% and 95% CL regions for ($n_s$, $r$), using observational data sets with and without a running spectral index, compared to the theoretical prediction of the model (73) with $n=2$. The black dashed line is for the case where model parameter $\alpha =0$ while gray and brown are for the case where $\alpha =-2\times 10^{-6}$ and $\alpha =1.5\times 10^{-6}$, respectively. The pairs of red and green dots represent the number of $e$-folds, $N=50$ and $N=60$, respectively.

Figure 6

Marginalized joint 68% and 95% CL regions for ($n_s$, $r$), using observational data sets with and without a running spectral index, compared to the theoretical prediction of the model (73) with $n=4$. The black dashed line is for the case where model parameter $\alpha =0$ while gray and brown are for the case where $\alpha =-0.7\times 10^{-12}$ and $\alpha =1.5\times 10^{-12}$, respectively. The pairs of red and green dots represent the number of $e$-folds, $N=50$ and $N=60$, respectively.

Figure 7

$n_s$ vs $d{n}_s/d\ln k$ plot, with observational data sets (left) and without observational data sets (right), compared to the theoretical prediction of the model (73) with $n=1$. The black dashed line is for the case where model parameter $\alpha =0$ while orange and blue are for the case where $\alpha =-0.003$ and $\alpha =0.001$, respectively. The pairs of red and green markers represent the number of $e$-folds, $N=50$ and $N=60$, respectively.

Figure 8

$n_s$ vs $d{n}_s/d\ln k$ plot, with observational data sets (left) and without observational data sets (right), compared to the theoretical prediction of the model (73) with $n=2$. The black dashed line is for the case where model parameter $\alpha =0$ while orange and blue are for the case where $\alpha =-2\times 10^{-6}$ and $\alpha =1.5\times 10^{-6}$, respectively. The pairs of red and green markers represent the number of $e$-folds, $N=50$ and $N=60$, respectively.

Figure 9

$n_s$ vs $d{n}_s/d\ln k$ plot, with observational data sets (left) and without observational data sets (right), compared to the theoretical prediction of the model (73) with $n=4$. The black dashed line is for the case where model parameter $\alpha =0$ while orange and blue are for the case where $\alpha =-10^{-12}$ and $\alpha =2.5\times 10^{-12}$, respectively. The pairs of red and green markers represent the number of $e$-folds, $N=50$ and $N=60$, respectively.