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We report the absorption and photoluminescence (PL) properties of InAsN alloys grown by gas source molecular beam epitaxy. A calculation based on the band anticrossing model was used to evaluate the Burstein-Moss effect and the band renormalization effect due to the high residual carrier density in the alloy and also the original band gap energy. It can be seen from our calculation that the broad linewidths of the PL spectra are due to the Burstein-Moss effect, and the high-energy edges of these spectra are consistent with the results from absorption measurements. The low-energy edges of PL spectra are also shown to be close to the calculated original band gap energy.