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Context: Fast radio bursts are transient radio pulses of extragalacticorigin. Their dispersion measure is indicative of the baryon content in theionized intergalactic medium between the source and the observer. However,inference using unlocalized fast radio bursts is degenerate to the distributionof redshifts of host galaxies. Method: We perform a joint inference of theintergalactic baryon content and the fast radio burst redshift distributionwith the use of Bayesian statistics by comparing the likelihood of differentmodels to reproduce the observed statistics in order to infer the most likelymodels. In addition to two models of the intergalactic medium, we considercontributions from the local environment of the source, assumed to be amagnetar, as well as a representative ensemble of host and interveninggalaxies. Results: Assuming that the missing baryons reside in the ionizedintergalactic medium, our results suggest that the redshift distribution ofobserved fast radio bursts peaks at $z \lesssim 0.6$. However, conclusions fromdifferent instruments regarding the intergalactic baryon content diverge andthus require additional changes to the observed distribution of host redshifts,beyond those caused by telescope selection effects.

Joint inference on the redshift distribution of fast radio burst and on the intergalactic baryon content