Observational constraints on braneworld inflation: The effect of a Gauss-Bonnet term

High-energy modifications to general relativity introduce changes to the perturbations generated during inflation, and the latest high-precision cosmological data can be used to place constraints on such modified inflation models. Recently it was shown that Randall-Sundrum–type braneworld inflation leads to tighter constraints on quadratic and quartic potentials than in general relativity. We investigate how this changes with a Gauss-Bonnet correction term, which can be motivated by string theory. Randall-Sundrum models preserve the standard consistency relation between the tensor spectral index and the tensor-to-scalar ratio. The Gauss-Bonnet term breaks this relation, and also modifies the dynamics and perturbation amplitudes at high energies. We find that the Gauss-Bonnet term tends to soften the Randall-Sundrum constraints. The observational compatibility of the quadratic potential is strongly improved. For a broad range of energy scales, the quartic potential is rescued from marginal rejection. Steep inflation driven by an exponential potential is excluded in the Randall-Sundrum case, but the Gauss-Bonnet term leads to marginal compatibility for sufficient e-folds.

Figure 1

The dependence of the slow-roll parameter $ϵ$ on $\chi$ [see Eq. (19)] for (a) $p=2$, (b) $p=4$ and (c) $p\to \infty$.

Figure 2

The dependence of $ϵ$ on ${\chi }_N$, for $N=60$ and (a) $p=2$, (b) $p=4$, (c) $p\to \infty$.

Figure 3

The dependence of $\eta$ on ${\chi }_N$, for $N=60$ and (a) $p=2$, (b) $p=4$, (c) $p\to \infty$.

Figure 4

The behavior of $-n_{\mathrm{T}}/ϵ$ as a function of the energy scale of inflation, $x=H/\mu$. The dashed curve is $\beta =0$, the solid curve is for $\beta ={10}^{-2}$.

Figure 5

2D posterior constraints in the $n_{\mathrm{S}}\mathrm{\text{−}}R$ plane with the $1\sigma$ and $2\sigma$ contour bounds. The solid curve is obtained by using the consistency relation $R=-16n_{\mathrm{T}}$ in the GB limit, whereas the dashed curve corresponds to $R=-8n_{\mathrm{T}}$ in the RS/GR cases.

Figure 6

The dependence of the quantity ${\beta }^3\sigma /64{\kappa }_4^2{\mu }^6$ on ${\chi }_N$ for (a) $p=2$, (b) $p=4$, (c) $p\to \infty$. We also show the quantum gravity limit curve, Eq. (47). The allowed region is above and to the left of this curve.

Figure 7

The spectral index $n_{\mathrm{S}}$ as a function of ${\chi }_N$ when $N=60$, for (a) $p=2$, (b) $p=4$, (c) $p\to \infty$.

Figure 8

The tensor-to-scalar ratio $R$ as a function of ${\chi }_N$ when $N=60$, for (a) $p=2$, (b) $p=4$, (c) $p\to \infty$ (solid curves). The dotted curves are obtained from $R=16ϵ$, which only holds in the GB limit.

Figure 9

Theoretical prediction of Gauss-Bonnet monomial inflation models for $N=50$, together with the $1\sigma$ and $2\sigma$ observational contour bounds. The left edge point of the theoretical curves is the RS limit, ${\chi }_N\ll 1$, and ${\chi }_N$ increases along the curves up to the quantum gravity limit. The curves are shown for (a) $p=2$, (b) $p=4$, (c) $p\to \infty$.

Figure 10

As in Fig. 9, with $N=60$.