Characterizing the equivalence between dark energy and radiation using gamma-ray bursts

Abstract

Differently from the equivalence time between either matter and radiation or dark energy and matter, the equivalence between dark energy and radiation occurs between two subdominant fluids, since it takes place in the matter dominated epoch. However, dark energy--radiation equivalence may correspond to a \emph{cosmographic bound} since it strongly depends on how dark energy evolves. Accordingly, a possible model-independent bound on this time would give hints on how dark energy evolves in time. In this respect, gamma-ray bursts (GRBs) may be used, in fact, as tracers to obtain cosmic constraints on this equivalence. Consequently, based on observed GR data from the $E_{\rm p}$--$E_{\rm iso}$ correlation, we here go beyond by simulating additional GRB data points and investigating two distinct equivalence epochs: 1) dark energy--radiation, and 2) dark energy--radiation with matter. We thus extract constraints on the corresponding two redshifts adopting Monte Carlo Markov chain simulations by means of two methods: the first performing the GRB calibration and the cosmological fit steps independently, and the second performing these steps simultaneously by resorting a hierarchical Bayesian regression. To keep the analysis model-independent, we consider a generic dark energy model, with the unique constraint to reduce to the $\Lambda$CDM at $z=0$. Our findings are thus compared to theoretical predictions, indicating that the $\Lambda$CDM model is statistically favored to predict such an equivalence time, though a slow evolution with time cannot be fully excluded. Finally, we critically re-examine the Hubble constant tension in view of our outcomes.