I am stuck varying an action.(adsbygoogle = window.adsbygoogle || []).push({});

This is the action [itex]S=\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2)[/itex]

And this is the solution, [itex]\ddot{h} + 2 \frac{\dot{a}}{a}\dot{h} - \nabla^{2}h [/itex].

This is what I get [itex]\partial_{0}(a^{2}\partial_{0}h)-\partial_{0}(a^{2}\nabla h)-\nabla(a^{2}\partial_{0}h)+\nabla^{2}(ha^{2})[/itex]

I don't really see my mistake, perhaps i am missing something. (dot represents [itex]\partial_{0}[/itex])

It is this problem (see Lectures on the Theory of Cosmological

Perturbations, by Brandenburger)

Going from step 91 to 92

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# Gravitational wave equation in FR sapace

Can you offer guidance or do you also need help?

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