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dingo_d
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Homework Statement
Using Friedmann equations find the parameter of deceleration [itex]q_0[/itex] using relative densities [itex]\Omega_M,\ \Omega_R,\ \Omega_\Lambda[/itex].
Homework Equations
Friedmann equations, deceleration parameter:
[itex]q_0=-\frac{\ddot{a_0}a_0}{\dot{a_0}^2}[/itex]
The Attempt at a Solution
So from second Friedmann equation (the one with k parameter which tells us whether the Universe is open, flat or close) and got to this point:
[tex]\left(\frac{\dot{a}}{\dot{a_0}}\right)^2 = \left(\frac{a_0}{a}\right)^2\Omega_R+\left(\frac{a_0}{a}\right)\Omega_M+\Omega_K+\left(\frac{a}{a_0}\right)^2\Omega_\Lambda[/tex]
a is the scale factor (sometimes denoted as R in the books).
And I'm stuck. The book here
equation (11.55)
Says that I should get
[itex]q=\frac{\Omega_M}{2}+\Omega_R-\Omega_\Lambda[/itex]
I tried using first Friedmann equation, but then my equation depends on parameter w, which connects pressure and density: [itex]p=w\rho[/itex], and I don't get correct answer :\
I found one presentation which says that I should somehow (no explanation, of course -.-") connect the equation I got with the deceleration parameter using: "a bit of math".
I tried connecting the second derivative of the scale factor in the definition of deceleration parameter, so that I don't need to use the equation which has w in it, but I really have no idea what to do.
Any help would be appreciated...
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