Revision of upper bound on volume-filling intergalactic magnetic fields with LOFAR

Magnetic fields present in the Large Scale Structure (LSS) of the Universe change polarization of radio waves arriving from distant extragalactic sources through the effect of Faraday rotation. This effect has been recently used to detect magnetic field in the LSS filaments based on the Rotation Measure data of the LOFAR Two-Meter Sky Survey (LoTSS). We notice that the same data also constrain the strength of the volume-filling magnetic field in the voids of the LSS. We use the LoTSS data to to derive an improved upper bound on the volume-filling field. The new upper bound provides an order of magnitude improvement on the previous Faraday rotation bounds. The new Faraday Rotation bound on the scale-invariant field that may originate from the epoch of inflation is also an order of magnitude lower than the bound on such field derived from the anisotropy analysis of the Cosmic Microwave Background.