Съдържание

SAO 2020, Подбор за GeCAA · структурирани задачи — Задача 2. Cosmology

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Всички материали от SAO 2020

GeCAA Selection Test Structured Question Paper · 7 т.

Условие

In a flat, matter-dominated universe, the scale factor $a$ is described by the equation:

a = \left(\frac{t}{t_0}\right)^{2/3} \qquad (2)

where $t_0$ is the present age of the universe, at which $a = 1$ . A spectroscopic study of uranium/thorium content revealed the age of the galaxy to be 12.3 Gyr.

a Given that the galaxy was formed 500 million years after the Big Bang, what value of the Hubble Constant $H_0$ would be consistent with this estimate? [4 т.]

b Determine the corresponding value of the critical density as well. [3 т.]

If you may require it, the Friedmann equations are given by:

H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} \qquad (3)

You are also given that $\frac{d}{dx}(x^n) = nx^{n-1}$ .

Отговори

Решение

Оригинал в Архива: GeCAA Selection Test Structured Question Paper.pdf · официални решения: GeCAA Selection Test Structured Question Solutions.pdf