The Best Inflationary Models After Planck

TL;DR

The study tackles identifying the best inflationary models under Planck 2013 data by performing Bayesian model comparison across 193 slow-roll, single-field potentials with a fast evidence-calculation pipeline that pairs an inflationary effective likelihood with ASPIC and MultiNest. It finds that about 34% of models are strongly disfavoured and 26% are favored, with only 9% remaining favored when Bayesian complexity is accounted for, all corresponding to plateau-type potentials. The analysis highlights that Higgs and KMIII inflation sit near the top in evidence, but KMIII is not decisively preferred due to higher complexity. Overall, Planck data strongly support simple plateau-like single-field slow-roll scenarios, while ruling out a substantial portion of the broader inflationary landscape; the work also provides a framework for incorporating priors and complexities in high-dimensional model comparisons and motivates further exploration of reheating and conformal-inflation connections under future data.

Abstract

We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data, with the aim of establishing which models are favoured from a Bayesian perspective. Our calculations employ a new numerical pipeline interfacing an inflationary effective likelihood with the slow-roll library ASPIC and the nested sampling algorithm MULTINEST. The models considered represent a complete and systematic scan of the entire landscape of inflationary scenarios proposed so far. Our analysis singles out the most probable models (from an Occam's razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered. We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes. If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes. These shapes are all of the plateau type.

Figures (7)

• Figure 1: Two-dimensional marginalised posterior distributions of the slow-roll parameters ($P_*$, $\epsilon_{1}$, $\epsilon_{2}$, $\epsilon_{3}$) using the Planck 2013 data.
• Figure 2: Bayes factors (bars) and absolute upper bound to the Bayes factors (arrows) for the Encyclopædia Inflationaris inflationary scenarios, with Higgs inflation as the reference model (see the text for a more accurate description).
• Figure 3: Logarithm of the Bayes factor versus the number of unconstrained parameters $N^{\mathrm{uc}}$ for all the inflationary models investigated. The $N^{\mathrm{uc}}$ dimension allows us to disambiguate models with the same evidence, by preferring those with the smallest number of unconstrained (i.e., unnecessary) parameters. Optimal models are clustered around Higgs Inflation and have $N^{\mathrm{uc}} \simeq 0$ together with $B^{}_{\mathrm{HI}} \gtrsim 0$. The four plots (from upper left to bottom right) increasingly zoom into the "best region". Each model is represented by a filled circle for illustration purposes only, and the radius of a circle has no meaning.
• Figure 4: Histogram of the Encyclopædia Inflationaris models within the four Jeffreys' categories (inconclusive: blue, weakly disfavoured: red, moderately disfavoured: green and strongly disfavoured: yellow) and for different number of unconstrained parameters. The number of preferred models is $17$, corresponding to $9$ different types of potential.
• Figure 5: Evolution of the GMSSMI Bayes factor versus the upper bound $-\ell$ of the prior range on $\alpha$ for $\alpha>1$ and $\alpha<1$. The green squares and blue circles represent numerical values of the evidence. The dotted red curves represent the analytical laws giving the behaviour of the Bayes factor versus $-\ell$ for $-\ell \gtrsim \ell_{\mathrm{c}}^\mathrm{max}$ according to Eqs. (\ref{['eq:gmssipcalib']}) and (\ref{['eq:evidgmssmmell']}). These equations predict how the Bayes factor behaves with $-\ell$ and, therefore, can be used to extrapolate in regimes where $\alpha$ becomes of order one.