# Looking for analytical expression of Cosmic Variance - Poisson distribution?

I have an expression of Matter Angular power spectrum which can be computed numerically by a simple rectangular integration method (see below). I make appear in this expression the spectroscopic cosmological bias $$b_{s p}^{2}$$ and the Cosmic variance $$N^{C}$$.

$$\mathcal{D}_{\mathrm{gal}, \mathrm{sp}} =\left[\int_{l_{\min }}^{l_{\max }} C_{\ell, \mathrm{gal}, \mathrm{sp}}(\ell) \mathrm{d} \ell\right]+N^{C}=b_{s p}^{2}\left[\int_{l_{m i n}}^{l_{\max }} C_{\ell, \mathrm{DM}} \mathrm{d} \ell+N^{C}\right]=b_{s p}^{2}\left[\mathcal{D}_{\mathrm{DM}}+N^{C}\right] \\ \simeq \Delta \ell \sum_{i=1}^{n} C_{\ell, \mathrm{gal}, \mathrm{sp}}\left(\ell_{i}\right)+b_{s p}^{2} N^{C}$$

I have a code that computes the terms $$C_{\ell, \mathrm{gal}, \mathrm{sp}}\left(\ell_{i}\right)$$ for each multipole $$\ell_{i}$$. But to compute $$\mathcal{D}_{\mathrm{gal}, \mathrm{sp}}$$, I have also to compute the term $$b_{s p}^{2} N^{C}$$ and especially the Cosmic Variance $$N^{C}$$ :

The only documentation I have found is the following slide from Nico Hamaus :

But as you can see, I have no explicit expression for Cosmic Variance : Could I consider the relation $$\dfrac{\sigma_{p}}{P}=\dfrac{2}{N_{k}^{1/2}}$$ as a SNR (Signal Noise Ratio) ?

Which expression of Cosmic Variance could I use to compute the whole expression $$\mathcal{D}_{\mathrm{gal}, \mathrm{sp}}$$ ?