Type Ia supernovae data with scalar-tensor gravity
  We study the use of type Ia Supernovae (SNe Ia) in the context of
scalar-tensor theories of gravity, taking as a working example induced gravity,
equivalent to Jordan-Brans-Dicke theory. Winking at accurate and precision
cosmology, we test the correction introduced by a time variation of the
Newton's constant, predicted by scalar-tensor theories, on the SNe distance
modulus relation. We find that for induced gravity the coupling parameter is
constrained from $\xi < 0.0095$ (95\% CL) using Pantheon SNe data alone down to
$\xi < 0.00063$ (95\% CL) combining {\em Planck} DR3 CMB information together
with a compilation of BAO measurements from BOSS DR12 and SNe data. In this
minimal case the improvements in terms of constraints on the cosmological
parameters coming from the addition of SNe data to CMB and BAO measurements is
limited, $\sim7\%$ on the 95\% CL upper bound on $\xi$. Allowing for the value
of the gravitational constant today to depart from the Newton's constant, we
find that the addition of SNe further tightens the constraints obtained by CMB
and BAO data on the standard cosmological parameters and by 22\% on the
coupling parameter, i.e., $\xi < 0.00064$ at 95\% CL. We finally show that in
this class of modified gravity models the use a prior on the absolute magnitude
$M_B$ in combination with the Pantheon SNe sample leads to results which are
very consistent with those obtained by imposing a prior on $H_0$, as happens
for other {\em early} solutions which accommodate a larger value of $H_0$
compared to the $\Lambda$CDM results.
