Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm trying to understand the classical derivation of Friedmann equation but I'm missing one step.

So, I start with accelerations, where $a$ is a scale factor


$\ddot{a}=-\frac{4\pi G}{3}\rho a$

Now multiply both sides by $\dot{a}$, and here is the question: Why LHS is


share|cite|improve this question
up vote 0 down vote accepted

Not sure I see the problem.

$\frac{1}{2}\frac{{\rm d}}{{\rm d}t}\big((\dot{a})^{2}\big) = \frac{1}{2}*2*\dot{a}*\frac{{\rm d}}{{\rm d}t}\big(\dot{a}\big) = \dot{a}\ddot{a}$. Maybe you don't recognize the notation - a dot is often used to denote a time derivative. Thus two dots indicates a double time derivative.

share|cite|improve this answer
ok I see... the product rule ;p I tried to do it LHS->RHS, what I should do is just the product rule on the RHS, silly me... – Luke Apr 25 '13 at 1:59

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.