  In this work, we investigate Newtonian cosmologies with a time-varying
gravitational constant, $G(t)$. We examine whether such models can reproduce
the low-redshift cosmological observations without a cosmological constant, or
any other sort of explicit dark energy fluid. Starting with a modified Newton's
second law, where $G$ is taken as a function of time, we derive the first
Friedmann--Lema{\^i}tre equation, where a second parameter, $G^*$, appears as
the gravitational constant. This parameter is related to the original $G$ from
the second law, which remains in the acceleration equation. We use this
approach to reproduce various cosmological scenarios that are studied in the
literature, and we test these models with low-redshift probes: type-Ia
supernovae (SNIa), baryon acoustic oscillations, and cosmic chronometers,
taking also into account a possible change in the supernovae intrinsic
luminosity with redshift. As a result, we obtain several models with similar
$\chi^2$ values as the standard $\Lambda$CDM cosmology. When we allow for a
redshift-dependence of the SNIa intrinsic luminosity, a model with a $G$
exponentially decreasing to zero while remaining positive (model 4) can explain
the observations without acceleration. When we assume no redshift-dependence of
SNIa, the observations favour a negative $G$ at large scales, while $G^*$
remains positive for most of these models. We conclude that these models offer
interesting interpretations to the low-redshift cosmological observations,
without needing a dark energy term.
