[Paper Review] Inflation after Planck: and the winners are

Jérôme Martin|arXiv (Cornell University)|Dec 13, 2013

Cosmology and Gravitation Theories4 references3 citations

TL;DR

This paper uses Bayesian model comparison to rank single-field slow-roll inflation models using Planck 2013 CMB data, identifying the most favored models based on evidence and complexity. It finds that approximately 10% of inflationary scenarios—specifically 17 out of 193—are statistically preferred, significantly narrowing the viable inflationary landscape after data constraints.

ABSTRACT

We review the constraints that the recently released Cosmic Microwave Background (CMB) Planck data put on inflation and we argue that single field slow-roll inflationary scenarios (with minimal kinetic term) are favored. Then, within this class of models, by means of Bayesian inference, we show how one can rank the scenarios according to their performances, leading to the identification of ``the best models of inflation''.

Motivation & Objective

• To identify the most observationally favored inflationary models following the release of Planck 2013 CMB data.
• To apply Bayesian inference to rank single-field slow-roll inflation models based on their evidence and complexity.
• To reduce the vast landscape of inflationary models by statistically eliminating those less compatible with observational data.
• To provide a statistically consistent framework for model comparison in early-universe cosmology using CMB measurements.

Proposed method

• Uses Bayesian evidence to quantify how well each inflationary model explains the Planck 2013 data.
• Applies the Jeffreys scale to interpret Bayes factors and assess the strength of evidence for model comparison.
• Defines model complexity via the Bayesian complexity $ C_b^i $, derived from the number of unconstrained parameters.
• Compares all models against a reference model (the Starobinsky model) and then redefines the reference to the best-performing model.
• Employs the formula $ N_{\rm uc}^i = N_{\rm param}^i - C_b^i $ to identify models with minimal free parameters in the inconclusive evidence category.
• Uses the Encyclopædia Inflationaris database to systematically evaluate 193 inflationary models.

Experimental results

Research questions

• RQ1 Which single-field slow-roll inflation models are most strongly supported by Planck 2013 CMB data?
• RQ2 How can Bayesian model comparison be used to rank inflationary models in a statistically rigorous way?
• RQ3 What is the role of model complexity in distinguishing between well-performing and overfitting inflationary scenarios?
• RQ4 How many inflationary models can be ruled out or disfavored based on Planck data using Bayesian evidence?
• RQ5 What criteria can be used to identify the 'best' inflationary model beyond just fitting the data?

Key findings

• Single-field slow-roll inflation with minimal kinetic terms is observationally favored by Planck 2013 data.
• Approximately 26% of the 193 models (52 models) fall into the 'inconclusive' Bayes factor category, indicating they are among the best-performing.
• After applying the criterion $ 0 < N_{\rm uc}^i < 1 $, the number of preferred models is reduced to 17, or about 9% of the total.
• About 73% of the models are now considered disfavored or ruled out by the Planck data based on Bayesian evidence.
• The method successfully reduces the inflationary landscape by identifying a small subset of models with minimal complexity and strong evidence.
• The Bayesian complexity measure $ C_b^i $ provides a useful but limited tool, especially when models deviate significantly from Gaussian statistics.