Hubble diagrams of relativistic broad-lined type Ic supernovae
  This paper is a demonstration of how relativistic, broad-lined type Ic
supernovae (SNe IcBL) can be used to constrain a value of the Hubble constant
in the local universe ($H_{0}$). Included in our sample of SNe IcBL are the SNe
associated with long-duration $\gamma$-ray bursts (GRB-SNe), as well as local
relativistic SNe IcBL that are not associated with GRBs. Building upon recent
results that found a luminosity$-$stretch relationship for a sample of nine
GRB-SNe, we demonstrate that GRB-SNe and SNe IcBL have statistically
significant luminosity$-$decline relationships in $BVR$ filters at the $p=0.02$
confidence level. Conversely, we show that SNe Ib, Ic and IIb do not have
statistically significant luminosity$-$decline relationships. Two of the
relativistic SNe IcBL in our sample have independent distance measurements (SN
2009bb and SN 2012ap) that we used to constrain a weighted-average value of
${H}_{0,\rm w}=82.5\pm8.1$ km s$^{-1}$ Mpc$^{-1}$. This value is 1$\sigma$
greater than that obtained using SNe Ia, and 2$\sigma$ larger than that
determined by Planck. This difference can be attributed to large peculiar
motions of the host galaxies of the two SNe IcBL, which are members of galaxy
groups. When determining a value of $H_{0}$ using SNe Ib, Ic and IIb, we found
an average value of $H_{0}$ that has a standard deviation of order $20-40$ km
s$^{-1}$ Mpc$^{-1}$, which demonstrates that these SNe are poor cosmological
candles. With the launch of the next generation of space telescopes, SNe IcBL,
and in particular GRB-SNe, have the potential to constrain constrain the Hubble
diagram up to a redshift of $z=3-5$.
