# Time reversal symmetry of the scale factor

In Barbara Ryden's Intro to Cosmology, in chapters 4.1 and 6.1, she states that $\dot{a}$ (or equivalently, $H(t)$) enters only as $\dot{a}^2$ in the Friedmann equation. She then deduce that a contraction phase is just the time reversal of the expansion phase. She then continues the chapter with taking only the positive root of $\dot{a}^2$.

A few questions:

1. What is the explanation that $\dot{a}^2$ in an equation implies that contraction is the time reversal of expansion?

2. Given that, why can we ignore the negative root of the Friedmann equation?