Using the Extragalactic Gamma-Ray Background to Constrain the Hubble Constant and Matter Density of the Universe

The attenuation produced by extragalactic background light (EBL) in $\gamma$-ray spectra of blazars has been used to constrain the Hubble constant ($H_0$) and matter density ($\Omega_{\rm m}$) of the Universe. We propose to estimate $H_0$ and $\Omega_{\rm m}$ using the well measured $>$10 GeV extragalactic $\gamma$-ray background (EGB). This suggestion is based on the facts that the $>$10 GeV EGB is totally explained by the emissions from blazars, and an EBL-absorption cutoff occurs at $\sim$50 GeV in the EGB spectrum. We fit the $>$10 GeV EGB data with modeled EGB spectrum. This results in $H_0=64.9^{+4.6}_{-4.3}\rm \ km\ s^{-1}\ Mpc^{-1}$ and $\Omega_{\rm m}=0.31^{+0.13}_{-0.14}$. Note that the uncertainties may be underestimated due to the limit of our realization for EBL model. $H_0$ and $\Omega_{\rm m}$ are degenerate in our method. Independent determination of $\Omega_{\rm m}$ by other methods would improve the constraint on $H_0$.