Scope: Lectures 01-02 · Purpose: Implement E(z), integrate D_C, derive D_L and D_A, and validate units and limiting behavior.
Setup and data
- Python 3.14.6 with the pinned requirements; no network needed.
- Use H0=67.4 km s^-1 Mpc^-1 and Omega_m=0.315 as a stated flat-LCDM teaching fiducial.
- Compare your quadrature result to the supplied Astropy check with Tcmb0=0 K so both models omit radiation.
Procedure
- Run the package self-test and record versions.
- Implement E(z) and test E(0)=1 and positivity over 0<=z<=2.
- Integrate D_C at z=0.1, 0.38, 0.51, 0.61, and 1.0; report quadrature tolerance.
- Derive D_L and D_A independently from reciprocity and check D_L=(1+z)^2 D_A.
- Compare z=1 D_L to Astropy; report absolute and fractional difference.
- Explain why the same late-time integrator is not a precision recombination model.
Deliverables
Deliver: source code, a machine-readable table, a one-page method note, unit tests, and a 150-word limitations section.
Assessment criteria
Rubric: equations/assumptions 20%; implementation and units 25%; independent validation 20%; convergence/error evidence 20%; interpretation and reproducibility 15%.
Uncertainty and interpretation
Report numerical precision, input uncertainty, model assumptions, and covariance availability separately. Label every output as directly measured, published summary, derived, or model/synthetic. A successful script run is not evidence that the scientific interpretation is valid.
Revisions and resubmissions are encouraged. Credit is based on defensible reasoning, validation, provenance, and clear limitations.