  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 $n_B \in (-3; -1.5)$.
