  A gravitational field model based on two symmetric tensors, $g_{\mu \nu}$ and
$\tilde{g}_{\mu \nu}$, is studied, using a Markov Chain Monte Carlo (MCMC)
analysis with the most updated catalog of SN-Ia. In this model, new matter
fields are added to the original matter fields, motivated by an additional
symmetry ($\tilde{\delta}$~symmetry). We call them $\tilde{\delta}$ matter
fields. This theory predicts an accelerating Universe without the need to
introduce a cosmological constant $\Lambda$ by hand in the equations. We
obtained a very good fit to the SN-Ia Data, and with this, we found the two
free parameters of the theory called $C$ and $L_2$. With these values, we have
fixed all the degrees of freedom in the model. The last $H_0$ local value
measurement is in tension with the CMB Data from Planck. Based on an absolute
magnitude $M_V = -19.23$ for the SN, Delta Gravity finds $H_0$ to be $74.47\pm
1.63$ km/(s Mpc). This value is in concordance with the last measurement of the
$H_0$ local value, $73.83\pm 1.48$ km/(s Mpc).
