What is the jerk parameter in terms of the Density parameters?

[Arman777]

In cosmology the deceleration parameter defined as the

$$q_0 = \frac{1}{2}\sum_i\Omega_{i,0}(1+3w_i)$$

Is there a similar expression for the jerk parameter ($j_0$) ?

 

[Arman777]

Here is the asnwer

In general

$$j(q) = q + 2q^2 + (1+z)\frac{dq}{dz}$$

for $\Lambda$CDM model$$j_0 = q_0 + 2q_0^2 + 1$$

Note that for different cosmological models

$$j_0 \neq q_0 + 2q_0^2 + 1$$

since in the other models $w_{\rm DE}$ is time dependent (well at least in most of them)