2016年IOAA理论第3题-早期宇宙
英文原题
(T3) Early Universe
Cosmological models indicate that radiation energy density, 𝜌r , in the Universe is proportional to (1 + 𝑧) 4 , and the matter energy density, 𝜌m, is proportional to (1 + 𝑧) 3 , where 𝑧 is the redshift. The dimensionless density parameter, Ω, is given as Ω = 𝜌/𝜌c , where 𝜌c is the critical energy density of the Universe. In the present Universe, the density parameters corresponding to radiation and matter, are Ωr0 = 10−4 and Ωm0 = 0.3, respectively.
(T3.1) Calculate the redshift, 𝑧e , at which radiation and matter energy densities were equal.
(T3.2) Assuming that the radiation from the early Universe has a blackbody spectrum with a temperature of 2.732 K, estimate the temperature, 𝑇e , of the radiation at redshift 𝑧e . (T3.3) Estimate the typical photon energy, 𝐸ν (in eV), of the radiation as emitted at redshift 𝑧e .
