2011

The background radiation in the young Universe

Round: Theory
Points: 10
Level: Bronze
Taught in: Section 13.2

Adapted from IOAA 2011 (Katowice), theory problem 15. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.

The cosmic background radiation has kept a blackbody spectrum throughout the history of the Universe. Find how its temperature depends on redshift, and give its temperature at $z \approx 10$ , the redshift of the furthest objects then known. The present temperature of the background radiation is 2.73 K.

I solved it without the solution

AnswerThe temperature grows as $T = T_{0} (1 + z)$ , and at $z = 10$ it was about 30.0 K.

This problem also appears among the olympiad problems of Section 13.2, Redshift and the scale factor, which teaches the ideas it uses. Equation and figure numbers refer to the course.