Constraining deviations from $Λ$CDM in the Hubble expansion rate

Abstract

The $Λ$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 $Λ$CDM framework. We explore a phenomenological model that quantifies the deviation of the Hubble expansion rate from the standard scenario, which is expressed as $H^{2}(z) = H^{2}_{\rm ΛCDM}(Ω_m, z)[1+δ(z)]$. We consider three distinct forms for the deviation parameter $δ(z)$: in model I, $δ(z)=δ_c$; in model II, $δ(z)=δ_{c}z/(1+z)$, and in model III, $δ(z)=δ_{c}{\rm ln}(1+z)$. Here, $δ_c$ represents a constant value. We utilize a comprehensive set of observational data to constrain the models. Our results show that for most combined datasets, $δ_c$ 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 $Λ$CDM model across all datasets examined. In contrast, model III exhibits a significant deviation from the $Λ$CDM model, exceeding $2σ$ for the full combined datastes. The AIC indicates that models I and II are consistent with the $Λ$CDM model, whereas model III is preferred over the standard $Λ$CDM model, with the $Λ$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 $Λ$CDM prediction.