Cosmological Parameters and Model Fitting
From Data to Parameters
Parameter estimation in practice
Modern cosmology is a parameter-inference science. Analysts compare theoretical predictions to datasets using likelihood functions, posterior distributions, and model selection criteria. Parameters often include , , , , the curvature , and the amplitude and tilt of the primordial spectrum.
Why degeneracies arise
Different combinations of parameters can produce very similar observables, so one dataset alone often cannot pin everything down.
Inference workflow
A typical analysis begins with a physical model, computes observables such as the CMB power spectrum or galaxy clustering signal, and then compares predictions to data. Bayesian methods are common because they allow priors, nuisance parameters, and uncertainty propagation to be handled consistently.
What does a likelihood function quantify?
The likelihood measures the probability of observing the data for specific parameter values.
Correct answer: How likely the data are given the model parameters
Name one parameter commonly inferred in cosmological analyses.
The Hubble constant is one of the key cosmological parameters inferred from multiple datasets.
Correct answer: H_0
How to compare two cosmological models
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1
Fit each model to the same datasets.
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2
Check parameter posteriors and residuals.
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3
Compare goodness-of-fit and complexity penalties.
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4
Assess whether added parameters are justified by the data.