Decay of $f(R)$ quintessence into dark matter: mitigating the Hubble tension?

Abstract

We propose a revised cosmological scenario that extends the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) framework by incorporating metric $f(R)$ gravity in the Jordan frame. In this model, the dark energy component arises from a non-minimally coupled scalar field, decomposed into a smooth background (set to unity to recover General Relativity) and a rapidly varying, massive fluctuation that decays into the dark matter sector. In the near-GR limit, this setup provides a phenomenological extension of $\Lambda$CDM characterized by two additional parameters: the present-day value of the scalar fluctuation and a normalized decay rate. Using a Markov Chain Monte Carlo analysis of low-redshift cosmological data, comprising Type Ia Supernovae, Baryon Acoustic Oscillation (BAO), and Cosmic Chronometer measurements, we find that the proposed model achieves a better overall fit than $\Lambda$CDM, while the Bayesian evidence remains statistically inconclusive given the inclusion of two extra parameters. The model predicts a moderate increase in the inferred value of $H_0$ and an improved consistency with DESI BAO data when adopting the SH0ES prior. Furthermore, describing dark matter particle creation as a transition phase in the late Universe offers an intriguing physical interpretation, potentially capturing features already present in current data and providing a promising avenue to explore extensions of the standard cosmological model within modified gravity frameworks.