Problem 1
Derive the central relation from Lectures 01-02. Define every symbol, state the coordinate system and approximation, and use the shared ASTR420 constants to obtain the requested scale. Show units through the final line.
Learning objectives
- Derive and apply a relativistic-cosmology relation.
- Analyze a traceable cosmology data extract.
- Communicate uncertainty and model dependence.
- Compare independent observational tests.
Instructions
Use SI units internally, report cosmological distances in Mpc or Gpc with the conversion shown, and distinguish a published input from a derived value. Submit calculations, a reproducible script/notebook, labeled figures, and a bibliography. Revisions are permitted within one week with a concise change note.
Problem 2
Use data/sn-hubble.csv to make one quantitative plot. Fit or transform the specified observable, report an uncertainty or residual statistic, and repeat after the prescribed sensitivity change. Include the exact input rows used.
Problem 3
A student claims that the plotted trend is a direct measurement of one cosmological component. Write a technically precise rebuttal distinguishing raw data, calibration, likelihood, model parameter, and an alternative explanation.
Problem 4
Transfer problem: compare the result with an independent probe from the neighboring unit. State whether the comparison is limited by statistical error, covariance, selection, calibration, or model dependence. A correct numerical ratio or direction is required where applicable.
Exact reading anchor
Chapter 29 Review Questions 1 and 3; Figuring for Yourself 29. The local extracted source index has chapter-label offsets near Chapter 29; verify exercise wording and numbering against the adopted PDF before assignment.
Deliverables
Four written solutions, one reproducible analysis, one uncertainty/sensitivity statement, and cited data provenance. Total: 100 points.