Constraining deviations from $\Lambda$CDM in the Hubble expansion rate

Abstract

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

arXiv comment13 pages, 1 figure, and 1 table. The European Physical Journal C (2025) 85:1350

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