[Paper Review] Cosmology: from theory to data, from data to theory

Florent Leclercq, Alice Pisani+1 more|arXiv (Cornell University)|Mar 5, 2014

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper presents a comprehensive framework for the interplay between cosmological theory and data, using Bayesian inference to analyze cosmic microwave background (CMB) and large-scale structure data. It establishes the highest-precision constraints to date on primordial non-Gaussianity, favoring single-field slow-roll inflation and ruling out several alternative models with high confidence.

ABSTRACT

Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental limits to cosmological knowledge?". We then describe the methodology for investigation: theoretical hypotheses are used to model, predict and anticipate results; data is used to infer theory. We illustrate with concrete examples of principled analysis approaches from the study of cosmic microwave background anisotropies and surveys of large-scale structure, culminating in a summary of the highest precision probe to date of the physical origin of cosmic structures: the Planck 2013 constraints on primordial non-Gaussianity.

Motivation & Objective

• To establish a principled methodology for the reciprocal flow of information between cosmological theory and observational data.
• To clarify the fundamental limits of what is observable and knowable in cosmology using causal diagrams and information theory.
• To apply Bayesian statistical methods to infer initial conditions from large-scale structure and to test inflationary models via primordial non-Gaussianity.
• To provide a rigorous statistical foundation for interpreting high-precision cosmological data, especially from Planck.
• To guide future observational strategies by identifying key uncertainties and testing theoretical paradigms.

Proposed method

• Utilizes causal diagrams to determine what information is directly or indirectly accessible in the causal structure of spacetime.
• Applies Gaussian random field theory to model primordial perturbations as the initial conditions for cosmic structure.
• Employs Bayesian inference for parameter estimation (first-level inference) and model comparison (second-level inference).
• Uses Markov Chain Monte Carlo (MCMC) techniques to explore posterior distributions in high-dimensional parameter spaces.
• Analyzes CMB bispectra and large-scale structure power spectra to detect deviations from Gaussianity in initial conditions.
• Applies non-linear Bayesian inference to reconstruct initial density fields from galaxy redshift surveys.

Experimental results

Research questions

• RQ1 What are the fundamental limits to cosmological knowledge due to causal structure and horizon constraints?
• RQ2 How can Bayesian statistics be systematically applied to infer cosmological parameters and compare models from observational data?
• RQ3 To what extent do current CMB and large-scale structure data support or rule out multi-field inflation and alternative early-universe scenarios?
• RQ4 What is the precise level of primordial non-Gaussianity, and how does it constrain inflationary physics?
• RQ5 How can initial conditions be reconstructed from present-day large-scale structure surveys using Bayesian methods?

Key findings

• The Planck 2013 constraints on primordial non-Gaussianity yield $f_{ ext{NL}}^{ ext{local}} = -0.9 /pm 5.1$, $f_{ ext{NL}}^{ ext{equilateral}} = -2.5 /pm 5.3$, and $f_{ ext{NL}}^{ ext{orthogonal}} = -25 /pm 39$, all consistent with Gaussian initial conditions.
• The constraint volume for the three main types of non-Gaussianity is 20 times smaller than pre-Planck, representing the highest-precision test to date of the origin of cosmic structures.
• Single-field slow-roll inflation models are strongly favored, with no evidence for non-Bunch-Davies initial states or significant multi-field contributions.
• The curvaton decay fraction is constrained to be at least 15% at 95% confidence, ruling out models with very small curvaton contributions.
• Models with a small speed of sound during inflation—such as DBI, $k$-inflation, and warm inflation—are ruled out, with $c_s \geq 0.02$ at 95% confidence.
• Ekpyrotic and cyclic models with exponential potentials and entropic perturbation generation are strongly disfavored by the data.