Primordial quadrupole-induced polarisation from filamentary structures and galaxy clusters

We present the first computation of the Cosmic Microwave Background (CMB) polarisation power spectrum from galaxy clusters and filaments using hydrodynamical simulations of large scale structure. We give the $E$ and $B$ mode power spectra of the CMB quadrupole induced polarisation between $\ell \sim 560$ and 20000. We find that the contribution from warm ionised gas in filamentary structures dominates the polarised signal from galaxy clusters by more than one order of magnitude on large scales (below $\mathrm{\ell }\sim 1000$) and by a factor of about two on small scales ($\mathrm{\ell }\text{gsim}10000$). We study the dependence of the power spectra with ${\sigma }_8$. Assuming the power spectra vary like ${\sigma }_8^n$ we find $n=3.2-4.0$ for filaments and $n=3.5-4.6$ for clusters.