Inflaton or curvaton? Constraints on bimodal primordial spectra from mixed perturbations

We consider cosmic microwave background constraints on inflation models for which the primordial power spectrum is a mixture of perturbations generated by inflaton fluctuations and fluctuations in a curvaton field. If future experiments do not detect isocurvature modes or large non-Gaussianity, it will not be possible to directly distinguish inflaton and curvaton contributions. We investigate whether current and future data can instead constrain the relative contributions of the two sources. We model the spectrum with a bimodal form consisting of a sum of two independent power laws, with different spectral indices. We quantify the ability of current and upcoming data sets to constrain the difference $\Delta n$ in spectral indices, and relative fraction $f$ of the subdominant power spectrum at a pivot scale of $k_0=0.017\mathrm{Mp}{\mathrm{c}}^{-1}h$. Data sets selected are the WMAP 7-year data, alone and in conjunction with South Pole Telescope data, and a synthetic data set comparable to the upcoming Planck data set. We find that current data show no increase in quality of fit for a mixed inflaton/curvaton power spectrum, and a pure power-law spectrum is favored. The ability to constrain independent parameters such as the tensor/scalar ratio is not substantially affected by the additional parameters in the fit. Planck will be capable of placing significant constraints on the parameter space for a bimodal spectrum.

Figure 1

Depiction of $\alpha$ as a function of $\Delta n$ and $f$. Running is largest when both $\Delta n$ and $f$ are large.

Figure 2

Marginalized constraints in the effective $n_s-r$ plane for the bimodal spectrum for (a) WMAP7 and (b) $\mathrm{WMAP}7+\mathrm{SPT}$. For each data set we also include results from a power-law fit (dashed lines). The two sets of contours overlap in each case.

Figure 3

Marginalized constraints in the effective $n_s-r$ plane for the bimodal spectrum for a simulated Planck-precision data set, showing a power-law fit (dashed lines).

Figure 4

Marginalized constraints in the $\Delta n-f$ plane for (a) WMAP7, (b) $\mathrm{WMAP}7+\mathrm{SPT}$, and (c) projection for a Planck-precision CMB data set.

Figure 5

Marginalized constraints in the $\alpha -n_s$ plane for (a) WMAP7, (b) $\mathrm{WMAP}7+\mathrm{SPT}$ and (c) projection for Planck precision CMB data set.