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I'm struggling to derive the accelerated Friedmann equation (shame on me!)...

I'll tell you what I'm doing and maybe you can find where the mistake is.

First of all, we know that:

[tex] H^2 = \frac{\rho}{2M^2_p}+\frac{\Lambda}{3}[/tex]

Now, using the Einstein Equations and doing the trace of these, we get:

[tex]-R-4\Lambda = \frac{T}{M^2_p} = \frac{-\rho+3p}{M^2_p}[/tex]

Where [itex]R=6[ \frac{\ddot{a}}{a}+H^2][/itex].

Using this, I get:

[tex] \frac{\ddot{a}}{a} = -\Lambda - \frac{1}{6}\frac{\rho+3p}{M^2_p}[/tex]

The problem is that I shouldn't get a minus sing in the [itex] \Lambda [/itex] and divided by 3, but I just CAN'T see what I'm doing wrong, as you can see here:

http://ned.ipac.caltech.edu/level5/Carroll2/Carroll1_2.html

I've tried to look for a book that does this derivation but I haven't found any...

If you could help me I would really appreciate it!

Thanks

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# Struggling with Friedmann equations

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