Constraining primordial magnetic fields through large scale structure

We study primordial magnetic field effects on the matter perturbations in the Universe. We assume magnetic field generation prior to the big bang nucleosynthesis (BBN), i.e. during the radiation dominated epoch of the Universe expansion, but do not limit analysis by considering a particular magnetogenesis scenario. Contrary to previous studies, we limit the total magnetic field energy density and not the smoothed amplitude of the magnetic field at large (order of 1 Mpc) scales. We review several cosmological signatures, such as halos abundance, thermal Sunyaev Zel'dovich (tSZ) effect, and Lyman-$\alpha$ data. For a cross check we compare our limits with that obtained through the CMB faraday rotation effect and BBN. The limits are ranging between 1.5 nG and 4.5 nG for $n_B \in (-3; -1.5)$.