Hunting down the best model of inflation with Bayesian evidence

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current “best model of inflation.” The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power $p>4$ are strongly disfavored. The class of small field models as a whole has posterior odds of approximately $3:1$ when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.

Figure 1

Results for the Bayes factor between different inflationary models considered in the analysis. The names of the models are specified on the left of the figure. The Bayes factor are computed taking massive large field model as the reference model, and the results are given in the column on the right of the plot. The dotted vertical lines indicate the thresholds of weak, moderate, and strong evidence, as per Table .

Figure 2

Bayes factor versus the effective number of unconstrained parameters ($\Delta {\mathcal{C}}_{\mathrm{b}}$) for all large and small field models. The steeper LFI models are genuinely disfavored by the data, as all of their free parameters are well constrained. Small field models being favored by the evidence still have unconstrained parameters, and therefore it is too early to conclusively rule out shallower ($p<2$) large field models, despite the fact that they exhibit a slightly smaller Bayes factor.