The average temperature of the present universe is 2.7 K. What was the cosmic scale factor of the universe when the average temperature was 270 K?

The cosmic scale factor of the universe is inversely proportional to the temperature of the universe. This means that if the temperature of the universe increases, the cosmic scale factor decreases and vice versa.

Given that the average temperature of the present universe is 2.7 K and the cosmic scale factor is 1 (by definition), we can use these values to find the cosmic scale factor when the average temperature was 270 K.

The relationship between the temperature and the cosmic scale factor is given by:

T1 / T2 = a2 / a1

where:

• T1 is the temperature of the universe at time 1 (2.7 K in this case)
• T2 is the temperature of the universe at time 2 (270 K in this case)
• a1 is the cosmic scale factor at time 1 (1 in this case)
• a2 is the cosmic scale factor at time 2 (what we're trying to find)

Plugging in the given values, we get:

2.7 K / 270 K = 1 / a2

Solving for a2, we find that a2 = 2.7 K / 270 K = 0.01.

So, the cosmic scale factor of the universe when the average temperature was 270 K was 0.01.