Constraint on primordial magnetic fields in the light of ARCADE 2 and EDGES observations

We study the constraints on primordial magnetic fields (PMFs) in the light of the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) low-band observation and Absolute Radiometer for Cosmology, Astrophysics and Diffuse Emission (ARCADE 2). ARCADE 2 observation detected extra-galactic excess radio radiation in the frequency range 3–90 GHz. The enhancement in the radio radiation is also supported by the first station of the Long Wavelength Array (LWA1) in the frequency range 40–80 MHz. The presence of early radiation excess over the cosmic microwave background can not be completely ruled out, and it may explain the EDGES anomaly. In the presence of decaying PMFs, 21 cm differential brightness temperature can modify due to the heating of the gas by decaying magnetic fields, and we can constraint the magnetic fields. For excess radiation fraction (A<inf>r</inf>) to be LWA1 limit, we show that the upper bound on the present-day magnetic field strength, B, on the scale of 1 Mpc is ≲ 3.7 nG for spectral index n<inf>B</inf>= - 2.99. While for n<inf>B</inf>= - 1 , we get B≲ 1.1 × 10 ^{- 3} nG. We also discuss the effects of first stars on IGM gas evolution and the allowed value of B. For A<inf>r</inf> to be LWA1 limit, we get the upper constraint on magnetic field to be B(n<inf>B</inf>= - 2.99) ≲ 4.9 × 10 ^{- 1} nG and B(n<inf>B</inf>= - 1) ≲ 3.7 × 10 ^{- 5} nG. By decreasing excess radiation fraction below the LWA1 limit, we get a more stringent bound on B.