# CMB anisotropies and tightly coupled limit

Sorry if this is a technical question. I am studying the origin of CMB anisotropies and the tightly coupled limit of the Boltzmann equations. We have a fluid composed of ionized electrons and photons.

In this limit, I read that, in the Legendre expansion of $\Theta = \delta T / T$, in the Fourier space :

$$\Theta_{\ell}(k,t) = \int_{-1}^{1} \dfrac{d\mu}{2}P_{\ell} (\mu)\ \Theta(k,\mu,t)$$

only the monopole and dipole are non-zero. Why ?

I understand why very small scales are damped (essentially because the wavelength is much smaller than the damping scale that relates to mean free path, density and so on). But large scales are beyond horizon, so should have very little anisotropy ? And scales between sub-horizon scales and small damped scales should exist. As I see the things, $\Theta_{\ell}$ should be non zero only at medium scales, but here it's only $\ell =0,1$ that are non zero.

I think that I am confusing the wavelenght of perturbation with the order of multipole in Legendre expansion. For me, large scale = $\Theta_1 \to \Theta_{\ell\sim 10}$, etc, a bit like in the power spectrum.

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