Constraining the dispersion measure redshift relation with simulation-based inference

We use the dispersion measure (DM) of localised Fast Radio Bursts (FRBs) to constrain cosmological and host galaxy parameters using simulation-based inference (SBI) for the first time. By simulating the large-scale structure of the electron density with the Generator for Large-Scale Structure (GLASS), we generate log-normal realisations of the free electron density field, accurately capturing the correlations between different FRBs. For the host galaxy contribution, we rigorously test various models, including log-normal, truncated Gaussian and Gamma distributions, while modelling the Milky Way component using pulsar data. Through these simulations, we employ the truncated sequential neural posterior estimation method to obtain the posterior. Using current observational data, we successfully recover the amplitude of the DM-redshift relation, consistent with Planck, while also fitting both the mean host contribution and its shape. Notably, we find no clear preference for a specific model of the host galaxy contribution. Although SBI may not yet be strictly necessary for FRB inference, this work lays the groundwork for the future, as the increasing volume of FRB data will demand precise modelling of both the host and large-scale structure components. Our modular simulation pipeline offers flexibility, allowing for easy integration of improved models as they become available, ensuring scalability and adaptability for upcoming analyses using FRBs. The pipeline is made publicly available under https://github.com/koustav-konar/FastNeuralBurst.