In this paper we investigate magnetic fields generated in the early Universe .
These fields are important candidates at explaining the origin of astrophysical magnetism observed in galaxies and galaxy clusters , whose genesis is still by and large unclear .
Compared to the standard inflationary power spectrum , intermediate to small scales would experience further substantial matter clustering , were a cosmological magnetic field present prior to recombination .
As a consequence , the bias and redshift distribution of galaxies would also be modified .
Hitherto , primordial magnetic fields ( PMFs ) have been tested and constrained with a number of cosmological observables , e.g .
the cosmic microwave background radiation , galaxy clustering and , more recently , weak gravitational lensing .
Here , we explore the constraining potential of the density fluctuation bias induced by gravitational lensing magnification onto the galaxy-galaxy angular power spectrum .
Such an effect is known as magnification bias .
Compared to the usual galaxy clustering approach , magnification bias helps in lifting the pathological degeneracy present amongst power spectrum normalisation and galaxy bias .
This is because magnification bias cross-correlates galaxy number density fluctuations of nearby objects with weak lensing distortions of high-redshift sources .
Thus , it takes advantage of the gravitational deflection of light , which is insensitive to galaxy bias but powerful in constraining the density fluctuation amplitude .
To scrutinise the potentiality of this method , we adopt a deep and wide-field spectroscopic galaxy survey .
We show that magnification bias does contain important information on primordial magnetism , which will be useful in combination with galaxy clustering and shear .
We find we shall be able to rule out at 95.4 \% CL amplitudes of PMFs larger than 5 \times 10 ^ { -4 } \mathrm { nG } for values of the PMF power spectral index n _ { B } \sim 0 .