By quantitative cosmology I mean with real times, distances, expansion rates, horizons, CMB stationary observers etc , derived from the standard model fitted to data. I don't mean ideas about conditions shortly before or after the start of expansion, although that is very interesting too.(adsbygoogle = window.adsbygoogle || []).push({});

The question has been on my mind: how would you approach teaching that? Say you were tutoring some interested person. I'd like to hear other people's ideas. Probably thescale factoris the most important thing to get one's mind around.

There would be two main levels to choose from: with and without the Friedman equation. I want to focus on the WITHOUT case. To deal briefly with the other case: if the person you are tutoring were good with simple differential equations and you went WITH the Friedman then it seems fairly straightforward. The conceptual structure might be like this:

the stretch in light we can observe: S = 1+z = a_{now}/a_{then}.

the distance growth rate H = a'/a, obviously a reciprocal time or percentage growth rate.

the (energy equivalent) matter density ρ comprising ordinary matter&radiation plus dark matter

the spatial flat case of the Friedman: H^{2}- Λ/3 = [const] ρ

where the LHS is reciprocal time and the [const] converts energy density into reciprocal time.

The without-Friedman case seems like it's a lot more challenging: how do you wean learners away from purely verbal thinking and accustom them to quantities? You have to use quantitative EXAMPLES: get the learner used to seeing numbers and imagining the growth process in real terms rather than merely verbally. What sorts of examples would it be good to work through?

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# How would you teach quantitative cosmology? What examples to use?

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