In cosmological perturbation theory, it's hard to find papers that would expose the general principle to perturb physical quantities (metric, fluid pressure and density, speed...) up to the n-$n$th order. Given the first and second orders I've found, it seems that the perturbation terms follow a Taylor expansion. The reason behind it is not 100% clear to me and I am looking for an explanation of the link between perturbation theory and Taylor expansion (if that's the case). Also, is there a mathematical demonstration of why it should be of that form (or at least why it's the most optimal)? Links to papers/resources are welcome.
Also, if I write at the first order:
$G_{\mu\nu}+\delta G_{\mu\nu} = \frac{8\pi G}{c^4}\left(T_{\mu\nu} + \delta T_{\mu\nu}\right)$$$G_{\mu\nu}+\delta G_{\mu\nu} = \frac{8\pi G}{c^4}\left(T_{\mu\nu} + \delta T_{\mu\nu}\right).$$
What would be the formula for cosmological perturbations up to the n-$n$th order?
