Cosmology from very high energy $\gamma$-rays

In this work we study how the cosmological parameter, the Hubble constant $H_0$, can be constrained by observation of very high energy (VHE) $\gamma$-rays at the TeV scale. The VHE $\gamma$-rays experience attenuation by background radiation field through $e^+e^-$ pair production during the propagation in the intergalactic space. This effect is proportional to the distance that the VHE $\gamma$-rays go through. Therefore the absorption of TeV $\gamma$-rays can be taken as cosmological distance indicator to constrain the cosmological parameters. Two blazars Mrk 501 and 1ES 1101-232, which have relatively good spectra measurements by the atmospheric Cerenkov telescope, are studied to constrain $H_0$. The mechanism constraining the Hubble constant adopted here is very different from the previous methods such as the observations of type Ia supernovae and the cosmic microwave background. However, at $2\sigma$ level, our result is consistent with other methods.