Question

What will the temperature of the cosmic microwave background be when the average distances between galaxies are 1.7 times as large as they are today? (Hint: The peak wavelength of photons in the background will then also be 1.7 times as large as it is today.)

Answer 1

Answer:

$T'=1.58K$

Explanation:

As the Universe expands, the photons of the cosmic microwave background increase its wavelength, making its temperature inversely proportional to the scale factor of the Universe. That is, as the average distances between galaxies increase, the temperature of the cosmic microwave background decreases by the same factor. Therefore, the temperature when the distances between galaxies are 1.7 times as large as they are today will be:

$T'=\frac{T_{now}}{1.73}\\T'=\frac{2.725K}{1.73}\\T'=1.58K$