The excessive dispersion measure (DM) of fast radio bursts (FRBs) has been proposed to be a powerful tool to study intergalactic medium (IGM) and to perform cosmography. One issue is that the fraction of baryons in the IGM, f _IGM, is not properly constrained. Here, we propose a method of estimating f _IGM using a putative sample of FRBs with the measurements of both DM and luminosity distance d _L. The latter can be obtained if the FRB is associated with a distance indicator (e.g., a gamma-ray burst or a gravitational-wave event), or the redshift z of the FRB is measured and d _L at the corresponding z is available from other distance indicators (e.g., SNe Ia) at the same redshift. As d _L/DM essentially does not depend on cosmological parameters, our method can determine f _IGM independent of cosmological parameters. We parameterize f _IGM as a function of redshift and model the DM contribution from a host galaxy as a function of star formation rate. Assuming f _IGM has a mild evolution with redshift with a functional form and by means of Monte Carlo simulations, we show that an unbiased and cosmology-independent estimate of the present value of f _IGM with a ∼12% uncertainty can be obtained with 50 joint measurements of d _L and DM. In addition, such a method can also lead to a measurement of the mean value of DM contributed from the local host galaxy.

In this paper, we propose to estimate the spatial curvature of the universe and the cosmic opacity in a model-independent way with expansion rate measurements, H(z), and type Ia supernova (SNe Ia). On the one hand, using a nonparametric smoothing method Gaussian process, we reconstruct a function H(z) from opacity-free expansion rate measurements. Then, we integrate the H(z) to obtain distance modulus μ _H, which is dependent on the cosmic curvature. On the other hand, distances of SNe Ia can be determined by their photometric observations and thus are opacity-dependent. In our analysis, by confronting distance moduli μ _H with those obtained from SNe Ia, we achieve estimations for both the spatial curvature and the cosmic opacity without any assumptions for the cosmological model. Here, it should be noted that light curve fitting parameters, accounting for the distance estimation of SNe Ia, are determined in a global fit together with the cosmic opacity and spatial curvature to get rid of the dependence of these parameters on cosmology. In addition, we also investigate whether the inclusion of different priors for the present expansion rate (H ₀: global estimation, 67.74 ± 0.46 km s⁻¹ Mpc⁻¹, and local measurement, 73.24 ± 1.74 km s⁻¹ Mpc⁻¹) exert influence on the reconstructed H(z) and the following estimations of the spatial curvature and cosmic opacity. Results show that, in general, a spatially flat and transparent universe is preferred by the observations. Moreover, it is suggested that priors for H ₀ matter a lot. Finally, we find that there is a strong degeneracy between the curvature and the opacity.

We apply two methods, i.e., the Gaussian processes and the nonparametric smoothing procedure, to reconstruct the Hubble parameter $H(z)$ as a function of redshift from 15 measurements of the expansion rate obtained from age estimates of passively evolving galaxies. These reconstructions enable us to derive the luminosity distance to a certain redshift $z$, calibrate the light-curve fitting parameters accounting for the (unknown) intrinsic magnitude of type Ia supernova (SNe Ia), and construct cosmological model-independent Hubble diagrams of SNe Ia. In order to test the compatibility between the reconstructed functions of $H(z)$, we perform a statistical analysis considering the latest SNe Ia sample, the so-called joint light-curve compilation. We find that, for the Gaussian processes, the reconstructed functions of Hubble parameter versus redshift, and thus the following analysis on SNe Ia calibrations and cosmological implications, are sensitive to prior mean functions. However, for the nonparametric smoothing method, the reconstructed functions are not dependent on initial guess models, and consistently require high values of $H_0$, which are in excellent agreement with recent measurements of this quantity from Cepheids and other local distance indicators.