AdvancedIOAA style, adapted

When did acceleration begin?

For a flat universe with $\Omega_m = 0.31$ and $\Omega_\Lambda = 0.69$ , compute the present deceleration parameter $q_0$ and the redshift at which the expansion switched from decelerating to accelerating.

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Reading resources

Material that covers the physics behind this problem.

An Introduction to Modern AstrophysicsCarroll & Ostlie
The standard reference for olympiad-level astrophysics. Chapters 1-3 cover the celestial sphere, orbits and the magnitude system.
Textbook
Ohio State Astronomy Lecture NotesOhio State University
Clear university-level notes on stars, galaxies and cosmology with derivations you can follow line by line.
Lecture notes
Cosmology CalculatorEdward L. Wright (UCLA)
Converts redshift into distances, lookback time and scale factors. Use it to sanity-check cosmology answers.
Website