IOAA 2016, theory — Задача 3. Early Universe

Theoretical Examination · 10 т.

Условие

Cosmological models indicate that radiation energy density, $\rho_{\mathrm{r}}$, in the Universe is proportional to $(1+\mathrm{z})^{4}$, and the matter energy density, $\rho_{\mathrm{m}}$, is proportional to $(1+\mathrm{z})^{3}$, where $\mathrm{z}$ is the redshift. The dimensionless density parameter, $\Omega$, is given as $\Omega = \rho/\rho_{\mathrm{c}}$, where $\rho_{\mathrm{c}}$ is the critical energy density of the Universe. In the present Universe, the density parameters corresponding to radiation and matter, are $\Omega_{\mathrm{r_0}} = 10^{-4}$ and $\Omega_{\mathrm{m_0}} = 0.3$, respectively.

T3.1 Calculate the redshift, $\mathrm{z_e}$, at which radiation and matter energy densities were equal. [3 т.]

T3.2 Assuming that the radiation from the early Universe has a blackbody spectrum with a temperature of 2.732 K, estimate the temperature, $T_{\mathrm{e}}$, of the radiation at redshift $\mathrm{z_e}$. [4 т.]

T3.3 Estimate the typical photon energy, $E_{\nu}$ (in eV), of the radiation as emitted at redshift $\mathrm{z_e}$. [3 т.]

Решение

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Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf