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Can you explain me how I can obtain wave equation given a metric? For example, if I have this metric $$g_{μν}=diag(−e^{2a(t)},e^{2b(t)},e^{2b(t)},e^{2b(t)})$$, how can derive the relation $$\frac{1}{\sqrt{g}}\partial _t(g^{00}\sqrt{g}\partial _t \phi)+\frac{1}{\sqrt{g}}g^{ii}\partial ^2 \phi$$ where ##\phi=\phi (t)## is a scalar field? Moreover, from this equation the professor has derived a Bessel's equation in the form u¨+ταu=0. I don't understand... Thanks

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# Wave equation given a cosmological inflationary metric

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