Measuring the duration of inflation with the curvaton

Simple models of single-field inflation in the very early universe can generate the observed amplitude and scale dependence of the primordial density perturbation, but models with multiple fields can provide an equally good fit to current data. We show how future observations will be able to distinguish between currently favored models. If a curvaton field generates the primordial perturbations after inflation, we show how the total duration of inflation can be measured.

Figure 1

Bayesian evidence $\mathcal{Z}$ of the single-field (inflaton) and two-field (inflaton plus spectator) models (inside and below the shaded region, respectively) considered in this work. The plateau model (taken as the reference here) is robust with respect to the introduction of an additional field. Quartic inflation with a spectator field (where the total number of $e$-folds is written in parenthesis) has a higher evidence than its single-field version, but lower than the plateau model.

Figure 2

Marginal posterior distributions over the key observables from inflation for plateaulike inflation (blue, darker) and quartic inflation (orange, clearer) with a spectator field. In the quartic case, the posterior fraction below the lower (upper) dotted line has more than 90% (50%) of primordial density perturbations generated by the curvaton field. Post-2020 CMB experiments would likely distinguish between or rule out both scenarios in terms of $n_{\mathrm{S}}$ and $r$. In combination with LSS data, the typical value of $f_{\mathrm{NL}}=-5/4$ associated with the curvaton scenario could also be detected.

Figure 3

Marginal posterior over the total number of $e$-folds of inflation $N_{\mathrm{tot}}$ with a uniform prior, for quartic inflation with a spectator field, assuming negligible initial spectator field values (otherwise, this plot represents an upper bound on $N_{\mathrm{tot}}$). The upper limit corresponds approximately to the “self-reproducing” regime, $N_{\mathrm{tot}}\sim 6\times {10}^4$. The dotted line and the grey band are respectively the mean and 1-sigma confidence-level limit of a logarithmic Gaussian process interpolation with maximum-a-posteriori noise level, scale and correlation length [74]. The black dots and bars are the evidence and their errors computed with MultiNest.