Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 310 / 1 / b

Given the component parameters, solve the first-order equationA cosmic string network has $w=-1/3$, so $\rho \propto a^{-2}$ and $H\propto a^{-1}$. Therefore $\dot{a}$ is constant and a string-dominated expanding universe hasafter choosing the Big Bang as $t=0$.