We set limits on the presence of the synchrotron cosmic web through the cross-correlation of the 2.3 GHz S-PASS survey with a model of the local cosmic web derived from constrained magnetohydrodynamic ( MHD ) simulations .
The MHD simulation assumes cosmologically seeded magnetic fields amplified during large-scale structure formation , and a population of relativistic electrons/positrons from proton-proton collisions within the intergalactic medium .
We set a model-dependent 3 \sigma upper limit on the synchrotron surface brightness of 0.16 mJy arcmin ^ { -2 } at 2.3 GHz in filaments .
Extrapolating from magnetic field maps created from the simulation , we infer an upper limit ( density-weighted ) magnetic field of 0.03 ( 0.13 ) \mu G in filaments at the current epoch , and a limit on the primordial magnetic field ( PMF ) of B _ { PMF } < 1.0 nG .