Comprehensive analysis of the simplest curvaton model

We carry out a comprehensive analysis of the simplest curvaton model, which is based on two noninteracting massive fields. Our analysis encompasses cases where the inflaton and curvaton both contribute to observable perturbations, and where the curvaton itself drives a second period of inflation. We consider both power spectrum and non-Gaussianity observables, and focus on presenting constraints in model parameter space. The fully curvaton-dominated regime is in some tension with observational data, while an admixture of inflaton-generated perturbations improves the fit. The inflating curvaton regime mimics the predictions of Nflation. Some parts of parameter space permitted by power spectrum data are excluded by non-Gaussianity constraints. The recent BICEP2 results [P. A. R. Ade et al. (BICEP2 Collaboration), Phys. Rev. Lett. 112, 241101 (2014)], if confirmed as of predominantly primordial origin, require that the inflaton perturbations provide a significant fraction of the total perturbation, ruling out the usual curvaton scenario in which the inflaton perturbations are negligible, though not the admixture regime where both inflaton and curvaton contribute to the spectrum.

Figure 1

The prediction for $n_{\mathrm{S}}$ shown for two different ranges of parameters, and cut off where $n_{\mathrm{S}}$ goes above one. This figure takes $N_{\text{matter}}=20$.

Figure 2

The difference in $n_{\mathrm{S}}$ arising from taking $N_{\text{matter}}=20$ rather than $N_{*}=53$. By design they agree at the inflaton limit.

Figure 3

Requiring the fraction of curvaton energy density at decay to be physical ($0<r_{\text{dec}}<1$) excludes the region of small inflaton mass and large initial curvaton field.

Figure 4

Values of $f_{\mathrm{NL}}$ showing also the region cut off by the physical requirement $r_{\text{dec}}\le 1$ as in Fig. 3. The contour corresponds to the 95% confidence upper limit from Planck.

Figure 5

Combined constraints on model space for the fiducial value $N_{\text{matter}}=20$ (top) and extremal values $N_{\text{matter}}=0$ (bottom left) and $N_{\text{matter}}=40$ (bottom right) with limits shown at 95% confidence for $f_{\mathrm{NL}}=14$, $n_{\mathrm{S}}=0.98$, and we take $r=0.05$ as an indicative lower bound from BICEP2 [3]. Labels are shown to the side of the surface for which they apply. The allowed region lies between the two mostly vertical planes (non-Gaussianity on the left, physically allowed value of $r_{\text{dec}}$ on the right), and above the plane of constant spectral index, for large values of $m_{\sigma }$, and above the plane of $r=0.05$ for small curvaton mass. The upper surfaces of the cubes correspond to the inflaton limit $m_{\varphi }=m_{\text{single}}$ which is the maximum permitted in the model.

Figure 6

Region occupied by curvaton models allowing $N_{*}$ to vary between 50 and 60 in all cases. The area between the red lines is the region covered by the usual curvaton scenario when $m_{\sigma }\ll m_{\varphi }$. The blue lines set $m_{\sigma }=m_{\varphi }/2$ to show the effect of a massive curvaton. The horizontal green lines are the inflating curvaton regime, which mimics the predictions of Nflation.