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 ) .