Constraining deviations from $\hat{I}›$CDM in the Hubble expansion rate

Abstract

The $\hat{I}›$CDM cosmolgical model has long been regarded as highly successful in accurately describing a wide range of astronomical observations. However, numerous observational findings have also provided hints of discrepancies from the predictions of the $\hat{I}›$CDM framework. We explore a phenomenological model that quantifies the deviation of the Hubble expansion rate from the standard scenario, which is expressed as $H^2(z)=H_{\hat{\mathrm{I}}›\mathrm{CDM}}^2(\hat{I}{\text{c◯}}_m,z)[1+\hat{I}´(z)]$. We consider three distinct forms for the deviation parameter $\hat{I}´(z)$: in model I, $\hat{I}´(z)=\hat{I}{´}_c$; in model II, $\hat{I}´(z)=\hat{I}{´}_{c}z/(1+z)$, and in model III, $\hat{I}´(z)=\hat{I}{´}_c\ln (1+z)$. Here, $\hat{I}{´}_c$ represents a constant value. We utilize a comprehensive set of observational data to constrain the models. Our results show that for most combined datasets, $\hat{I}{´}_c$ tends to take on negative values for models I and II, while consistently taking positive values in model III. Furthermore, we find that both models I and II remain consistent with the standard $\hat{I}›$CDM model across all datasets examined. In contrast, model III exhibits a significant deviation from the $\hat{I}›$CDM model, exceeding $2\ddot{I}ƒ$ for the full combined datastes. The AIC indicates that models I and II are consistent with the $\hat{I}›$CDM model, whereas model III is preferred over the standard $\hat{I}›$CDM model, with the $\hat{I}›$CDM model being disfavored for the combined datasets DESI BAO + CMB + CC + DESY5. These results suggest that the Hubble expansion rate likely deviates from the standard $\hat{I}›$CDM prediction.

13 pages, 1 figure, and 1 table. The European Physical Journal C (2025) 85:1350