The two most precise gauges of the Universe’s expansion rate have recently been in glaring disagreement. The measurement of the Hubble parameter makes the Universe expansion theory more and more confusing, the cosmological redshift may not only be related to distance but also to other factors, and the expansion of the Universe may be just an illusion. The Compton effect of free electrons and low energy photons has been observed in the laboratory. This paper presents a theory: Free electron Compton scattering (FEC) may produce the illusion of the Universe expansion: Photons interact with a large number of free electrons on their way to us from a distant source. FEC causes photons to redshift (FEC redshift), and the photon beam expands along the propagation direction, these may produce the illusion of cosmic expansion (FEC cosmic model). FEC redshift is independent of wavelength, and proportional to distance and corresponding electron density, consistent with the Doppler effect of the expansion of the Universe. Flare redshift is a common phenomenon, and it is difficult to use the Doppler effect to explain alone, there is evidence of FEC redshift in flare redshift.