The decisive future of inflation

TL;DR

This paper introduces a novel Bayesian information-theoretic method to evaluate and optimize future inflationary model measurements, emphasizing the importance of spectral index precision over tensor ratio accuracy.

Contribution

It develops a new approach for assessing the utility of future cosmological surveys in inflationary model selection using Bayesian evidence and information theory.

Findings

Decreasing uncertainty in the scalar spectral index is more impactful than reducing tensor-to-scalar ratio uncertainty.

The method enables quantification of future experiments' ability to constrain reheating temperature and scalar running.

A publicly available Python tool, foxi, implements this approach for survey optimization.

Abstract

How much more will we learn about single-field inflationary models in the future? We address this question in the context of Bayesian design and information theory. We develop a novel method to compute the expected utility of deciding between models and apply it to a set of futuristic measurements. This necessarily requires one to evaluate the Bayesian evidence many thousands of times over, which is numerically challenging. We show how this can be done using a number of simplifying assumptions and discuss their validity. We also modify the form of the expected utility, as previously introduced in the literature in different contexts, in order to partition each possible future into either the rejection of models at the level of the maximum likelihood or the decision between models using Bayesian model comparison. We then quantify the ability of future experiments to constrain the reheating temperature and the scalar running. Our approach allows us to discuss possible strategies for maximising information from future cosmological surveys. In particular, our conclusions suggest that, in the context of inflationary model selection, a decrease in the measurement uncertainty of the scalar spectral index would be more decisive than a decrease in the uncertainty in the tensor-to-scalar ratio. We have incorporated our approach into a publicly available python class, foxi (https://sites.google.com/view/foxicode), that can be readily applied to any survey optimisation problem.