I have been reading the TASI Lectures on Inflation by William Kinney, (https://arxiv.org/pdf/0902.1529v2.pdf).(adsbygoogle = window.adsbygoogle || []).push({});

I came across the mode function eq (128) (which obeys a generalization of the Klein-Gordon equation to an expanding spacetime), as I read through until eq (163), I know that it is the Hankel function (though he said it is the bessel function to which it is the solution to the differential equation in eq (162)),

1) How did he get the normalization constant ##\sqrt{-kτ}##?

2) How can I get the order of the Bessel function ##ν##?

3) How did he simplify the mode function to eq (166)?

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# I Primordial power spectrum

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