ASTR 420 Lecture 14: Cosmological Synthesis, Tensions, and Tests

Terms Developed in Context

These terms form the lecture's reasoning chain from observable through model to a bounded physical conclusion.

Joint likelihood

The combined probability of multiple datasets given shared model parameters and stated dependence assumptions. In this lecture it supports the evidence-to-model chain for multi-probe consistency, covariance, model comparison, and open questions.

Use and relationship: Read it together with Concordance model and Covariance matrix. The governing relation \(\\chi^2=(\\mathbf d-\\mathbf m)^T C^{-1}(\\mathbf d-\\mathbf m)\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This summary is conditional on independent Gaussian errors; shared calibration or model covariance changes the interpretation. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Covariance matrix

A matrix encoding variances and correlated errors among measured quantities or fitted summaries. In this lecture it supports the evidence-to-model chain for multi-probe consistency, covariance, model comparison, and open questions.

Use and relationship: Read it together with Joint likelihood and Posterior tension. The governing relation \(\\chi^2=(\\mathbf d-\\mathbf m)^T C^{-1}(\\mathbf d-\\mathbf m)\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This summary is conditional on independent Gaussian errors; shared calibration or model covariance changes the interpretation. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Posterior tension

A quantified mismatch between parameter constraints after priors, likelihoods, and covariance are specified. In this lecture it supports the evidence-to-model chain for multi-probe consistency, covariance, model comparison, and open questions.

Use and relationship: Read it together with Covariance matrix and Model comparison. The governing relation \(\\chi^2=(\\mathbf d-\\mathbf m)^T C^{-1}(\\mathbf d-\\mathbf m)\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This summary is conditional on independent Gaussian errors; shared calibration or model covariance changes the interpretation. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Model comparison

The assessment of relative explanatory performance while accounting for fit quality, complexity, and prior assumptions. In this lecture it supports the evidence-to-model chain for multi-probe consistency, covariance, model comparison, and open questions.

Use and relationship: Read it together with Posterior tension and Concordance model. The governing relation \(\\chi^2=(\\mathbf d-\\mathbf m)^T C^{-1}(\\mathbf d-\\mathbf m)\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This summary is conditional on independent Gaussian errors; shared calibration or model covariance changes the interpretation. This caveat prevents the term from being treated as a unique explanation or a context-free number.

Concordance model

A cosmological model supported by mutually consistent constraints from several independent probes and epochs. In this lecture it supports the evidence-to-model chain for multi-probe consistency, covariance, model comparison, and open questions.

Use and relationship: Read it together with Model comparison and Joint likelihood. The governing relation \(\\chi^2=(\\mathbf d-\\mathbf m)^T C^{-1}(\\mathbf d-\\mathbf m)\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.

Boundary: This summary is conditional on independent Gaussian errors; shared calibration or model covariance changes the interpretation. This caveat prevents the term from being treated as a unique explanation or a context-free number.