Polynomial Chaotic Inflation in the Planck Era

Abstract

We propose a chaotic inflation model in supergravity based on polynomial interactions of the inflaton. Specifically we study the chaotic inflation model with quadratic, cubic and quartic couplings in the scalar potential and show that the predicted scalar spectral index and tensor-to-scalar ratio can lie within the 1 sigma region allowed by the Planck results.

Figures (4)

• Figure 1: The schematic picture of the scalar potential (\ref{['scalar']}).
• Figure 2: (Top) The prediction of polynomial chaotic inflation model is shown in $(n_s,r)$ plane for $N_e = 60$ (red, solid) and $50$ (red, dashed). In this plot we have taken $\theta = 23\pi/60$. Also shown are observational $1\sigma$ (dark) and $2\sigma$ (light) constraints from the Planck satellite Ade:2013rta: Planck + WMAP polarization (gray), Planck + WMAP polarization + high-$\ell$ CMB measurement (red), Planck + WMAP polarization + baryon acoustic oscillation (blue). Filled circles connected by line segments show the predictions from chaotic inflation with $V \propto \varphi^3$ (green), $\varphi^2$ (black), $\varphi$ (yellow), $\varphi^{2/3}$ (red) and $R^2$ inflation (orange), for $N_e=50$ (small circle)--$60$ (big circle). Purple band shows the prediction of natural inflation Ade:2013rta. (Bottom) Same as top panel, but for various values of $\theta$. Here we have taken $N_e=60$.
• Figure 3: The scalar spectral index as a function of $\varphi_t/M_P$ for $\theta = 23\pi/60$.
• Figure 4: The parameters $\lambda$ and $m$ (in Planck unit) which reproduce the Planck normalization of the CMB anisotropy for $\theta = 23\pi/60$.