Decay of dark energy into dark matter in a metric $f(R)$ gravity: effective running Hubble constant (2506.13288v1)

Abstract: We examine a modified late-Universe dynamics where dark energy decays into dark matter, within the framework of metric $f(R)$-gravity in the Jordan frame. After a detailed analysis of the modified $\Lambda \text{CDM}$ model, we introduce a theoretical diagnostic tool to capture the emergence of an effective running Hubble constant as a function of redshift. We then compare this theoretical model with the 40-bin analysis of the Supernova Pantheon sample. This comparison allows us to determine the value of the additional free parameter that appears in our model, beyond those of the standard $\Lambda \text{CDM}$ model. Our modified late Universe dynamics provides a good-quality fit to the binned data, improving upon the previous phenomenological interpretation based on a power-law decay. However, unlike the power-law model, our approach cannot be extrapolated to the recombination redshift to match the Hubble constant measured by the Planck satellite. In fact, the dynamics resulting from the binned Pantheon sample analysis address only weakly the Hubble tension between the SH0ES and the Planck Collaboration values of the Hubble constant. Here we provide a convincing representation of the observed deviation of the cosmological dynamics from the $\Lambda$CDM-one, as it out-stands from the low redshift observed sources.