Question

If the temperature of the background radiation today is 3k , at what time after the birth of universe was the temperature (10)15 k? Take the age of the universe as 15 * (10)9 years .

Answer 1

Answer on Question #45915, Physics, Astronomy — Astrophysics

If the temperature of the background radiation today is 3k , at what time after the birth of universe was the temperature (10)15 k? Take the age of the universe as 15 * (10)9 years.

Solution

We will take a simple cosmological model where scale factor a is related with time t as

$a\sim t^{2/3}$

Then, we know that $T\sim 1/a$ and temperature can be found as

$\frac{T_{0}}{T_{1}}=\frac{t_{1}^{2/3}}{t_{0}^{2/3}}$

And we find at what time it was $10^{15}$ K

$t_{1}=t_{0}\left(\frac{T_{0}}{T_{1}}\right)^{3/2}=15\cdot 10^{9}\left(\frac{3}{10^{15}}\right)\approx 2.5\cdot 10^{-12}\,s$

http://www.AssignmentExpert.com/