# Cosmology - given omega_m and a static universe, find the range of values of q_0

Hi there,

the full question is as follows:

Suppose omega_m = 0.2. If we observe cosmic acceleration at z=0, what is the possible range of values of q_0? What is the minimum value of lambda? What is omega_total?

so I'm having trouble with the relationship between q$_{0}$, $\Omega$$_{m,0}$, $\lambda$, and $\Omega$ $_{\lambda}$.

To be honest, i don't even really understand what q$_{0}$ represents.

I've found from a source that q$_{0}$=$\frac{1}{2}$$\Omega$$_{m,0}$-$\Omega$ $_{\lambda}$.

Could anyone explain to me how these all relate and possibly point me in the right direction here?

Thanks!

These are not homework questions and will never be submitted. My professor always gives us a bunch of practice problems that are representative of questions that will be on our quizzes. It is more important that we understand the point of the question rather than have a mathematical answer.

Remember the definition for deceleration parameter $q = -\frac{\ddot{a} a}{\dot{a}^2 } = -\frac{1}{H^2} \frac{\ddot{a}}{a}$. That should give you immediately answer to the first question. Then use the Friedmann equations to massage an useful expression for $\frac{\ddot{a}}{a}$