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The accelerated expansion of the universe implies the existence of an energy contribution known as dark energy. Associated with the cosmological constant in the standard model of cosmology, the nature of this dark energy is still unknown. We will discuss an alternative gravity model in which this dark energy contribution emerges naturally, as a result of allowing for a time-dependence on the gravitational constant, G, in Einstein's field equations. With this modification, Bianchi's identities require an additional tensor field to be introduced so that the usual conservation equation for matter and radiation is satisfied. The equation of state of this tensor field is obtained using additional constraints, coming from the assumption that this tensor field represents the space-time response to the variation of G. We will also present the predictions of this model for the late-universe data, and show that the energy contribution of this new tensor is able to explain the accelerated expansion of the universe without the addition of a cosmological constant. Unlike many other alternative gravities with varying gravitational strength, the predicted G evolution is also consistent with local observations and therefore this model does not require screening. We will finish by discussing possible other implications this approach might have for cosmology and some future prospects. [ABSTRACT FROM AUTHOR]

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–Lemaître 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 χ2 values as the standard ΛCDM 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. [ABSTRACT FROM AUTHOR]