Scope: Lectures 03-04. Four questions; submit derivations and code/output where requested.
State units and model assumptions. Keep unrounded values in code and round only in your final communication. Revisions and resubmissions are encouraged.
Question 1
At z=0.5 and z=1, calculate D_C, D_L, D_A, and mu using the supplied flat-LCDM integrator. Show the reciprocity check.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 2
For z=1, compare the computed mu to a hypothetical standardized observation 0.20 mag brighter. Estimate the fractional distance change using a first-order expansion and state its sign.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 3
Explain why changing H0 shifts the Hubble diagram's intercept while relative shape can still constrain expansion history.
Work to show: equations, units, assumptions, and a reproducible computation where requested.
Question 4
For an 18-row covariance-aware demonstration, list the dimensions and meaning of the covariance matrix. Explain why it is invalid to infer a Pantheon+ cosmological constraint from the excerpt.
Work to show: equations, units, assumptions, and a reproducible computation where requested.