Higgs $G$ inflation

A new class of inflation models within the context of G inflation is proposed, in which the standard model Higgs boson can act as an inflaton thanks to Galileon-like nonlinear derivative interaction. The generated primordial density perturbation is shown to be consistent with the present observational data. We also make a general discussion on potential-driven $G$-inflation models, and find a new consistency relation between the tensor-to-scalar ratio $r$ and the tensor spectral index $n_T$, $r=-32\sqrt{6}{n}_T/9$, which is crucial in discriminating the present models from standard inflation with a canonical kinetic term.

Figure 1

The Galileon effect operates above the straight line (magenta), and the slow-roll condition $ϵ<1$ is satisfied above the dashed line (cyan). Chaotic G inflation therefore takes place in the shaded region, while in the dotted region standard chaotic inflation occurs. In particular, in the filled region (brown) the potential is rather steep and hence standard inflation would not proceed, but G inflation can. For $M>M_c$ it can be seen that a standard inflationary phase follows G inflation.

Figure 2

The same diagram as Fig. 1, but for new and hybrid inflation with $|{\eta }_{\mathrm{std}}|<1$, is shown. The Galileon effect operates above the inclined straight line (magenta), the slow-roll condition $ϵ<1$ is satisfied below the dashed line (cyan), and the constant piece $V_0$ dominates the potential below the horizontal straight line (green).

Figure 3

The same diagram as Fig. 1, but for new and hybrid inflation with $|{\eta }_{\mathrm{std}}|>1$, is shown. The slow-roll conditions are satisfied below the $ϵ=1$ line and above the $\eta =1$ line. Therefore, even though ${\eta }_{\mathrm{std}}>1$, G inflation can occur in the shaded region (green).

Figure 4

The evolution of $|\varphi |$ [upper oscillating line (blue)] and $\rho$ [lower line (purple)] in the very final stage of Higgs G inflation and in the reheating stage thereafter is shown. We set $a(t_{\mathrm{end}})=1$ with $ϵ(t_{\mathrm{end}})=1$. The parameters are given by $\lambda =0.1$ and $M=0.01\times M_c$.